Monochromatic light of wavelength 1 is incident on a pair of slits separated by 2.15 x 10⁻⁴ m and forms an interference pattern on a screen placed 2.15 m from the slits. The first-order bright fringe is at a position Ypright = 4.56 mm measured from the center of the central maximum. From this information, we wish to predict where the fringe for n = 50 would be located. (a) Assuming the fringes are laid out linearly along the screen, find the position of the n = 50 fringe by multiplying the position of the n = 1 fringe by 50.0. (b) Find the tangent of the angle the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum. (c) Using the result of part (b) and dsin bright = ma, calculate the wavelength of the light. nm (d) Compute the angle for the 50th-order bright fringe from dsinê bright (e) Find the position of the 50th-order bright fringe on the screen from Ybright = Ltan bright (f) Comment on the agreement between the answers to parts (a) and (e).

Answers

Answer 1

For a monochromatic light

The position of the 50th order bright fringe is 228 mm.

The angle θ that the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum is 0.12°.

The wavelength of the light is 500 nm.

The angle made by the 50th-order bright fringe is 57.9°.

The position of the 50th-order bright fringe on the screen is 3.91 m.

For a monochromatic light

(a) To find the position of the 50th bright fringe, multiply the position of the 1st bright fringe by 50. The first-order bright fringe's position is given by Ybright = 4.56 mm.

Therefore, the position of the 50th order bright fringe is Y50bright = 50 × Ybright = 50 × 4.56 = 228 mm.

(b) The angle θ that the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum can be found using trigonometry. θ = tan⁻¹(Ybright / L) = tan⁻¹(4.56 mm / 2150 mm) = 0.12°

(c) The wavelength λ can be calculated using the relationship dsin bright = mλ, where d is the distance between the slits, bright is the angle made by the bright fringe with respect to the line extending from the point midway between the slits to the center of the central maximum, and m is the order of the bright fringe. We know that the distance between the slits is d = 2.15 × 10⁻⁴ m and that the angle made by the first-order bright fringe is bright = 0.12°. We need to convert this angle to radians before we can use it in the equation. Therefore, bright = 0.12° × (π / 180) = 0.00209 radians. Substituting these values into the equation and solving for λ givesλ = dsin bright / m = (2.15 × 10⁻⁴ m) × sin(0.00209) / 1 = 5.00 × 10⁻⁷ m = 500 nm.

(d) The angle made by the 50th-order bright fringe is given by bright = sin⁻¹(mb / d), where b is the distance from the center of the central maximum to the 50th-order bright fringe and m is the order of the bright fringe. We know that m = 50 and that d = 2.15 × 10⁻⁴ m. We need to find b. Using the relationship b = Ltan bright, where bright is the angle made by the bright fringe with respect to the line extending from the point midway between the slits to the center of the central maximum, we can find b. We know that bright = 50 × 0.12° = 6.00° and that L = 2.15 m. Therefore, b = Ltan bright = 2.15 m × tan(6.00°) = 0.24 m. Substituting these values into the equation and solving for bright givesbright = sin⁻¹(mb / d) = sin⁻¹(50 × 0.24 / 2.15 × 10⁻⁴) = 1.01 radians = 57.9°.

(e) The position of the 50th-order bright fringe on the screen is given by Y50bright = Ltan bright = 2.15 m × tan(57.9°) = 3.91 m.(f)

The answers to parts (a) and (e) agree because we have used the same method to calculate the position of the 50th-order bright fringe. In part (a), we multiplied the position of the 1st bright fringe by 50 to find the position of the 50th-order bright fringe. In part (e), we used the relationship Ybright = Ltan bright to find the position of the 50th-order bright fringe directly.

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Related Questions

20 pts) A system is described by the differential equation below and assuming all initial conditions are zero, dy(t) dt dx(t) dt find the transfer function, H(s), Y(s), and y(t) for x(t) = u(t). Is the system stable? d²y(t) dt² +10 ! + 24 y(t) = + x(t)

Answers

The transfer function, H(s), and output, Y(s), were found by taking the Laplace transform of the given differential equation and using partial fraction decomposition. The output in the time domain, y(t), was found by taking the inverse Laplace transform. The system is stable because all the poles of the transfer function have negative real parts.

To find the transfer function, H(s), we can take the Laplace transform of the differential equation and rearrange it as follows:

s²Y(s) + 10sY(s) + 24Y(s) = X(s)

H(s) = Y(s)/X(s) = 1/(s² + 10s + 24)

To find Y(s), we can multiply both sides of the transfer function by X(s) and use partial fraction decomposition:

Y(s) = X(s)H(s) = X(s)/(s² + 10s + 24) = A/(s + 4) + B/(s + 6)

where A and B are constants that can be solved for using algebraic manipulation. In this case, we have:

X(s) = 1/s

A/(s + 4) + B/(s + 6) = 1/(s² + 10s + 24)

Multiplying both sides by (s + 4)(s + 6), we get:

A(s + 6) + B(s + 4) = 1

Substituting s = -4, we get:

A = -1/2

Substituting s = -6, we get:

B = 3/2

Therefore, the output Y(s) is:

Y(s) = (-1/2)/(s + 4) + (3/2)/(s + 6)

To find y(t), we can take the inverse Laplace transform of Y(s):

y(t) = (-1/2)e^(-4t) + (3/2)e^(-6t)

The system is stable because all the poles of the transfer function have negative real parts. Specifically, the poles are at s = -4 and s = -6, which correspond to exponential decay terms in the output.

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What is the time constant? s (b) How long will it take to reduce the voltage on the capacitor to 0.100% of its full value once discharge begins? s (c) If the capacitor is charged to a voltage V 0

through a 133Ω resistance, calculate the time it takes to rise to 0.865V 0

(this is about two time constants). S

Answers

Therefore, it takes approximately 26.4 seconds to rise to 0.865V0.

Time ConstantIt is the time required by an electric circuit or system to change its state from an initial state to its final state after an abrupt change in one of its variables. The transient response of the circuit or system is characterized by the time constant.

The formula for the time constant in seconds is given by the product of the resistance and the capacitance, i.e.,T=RC(a) To determine the time it takes for the capacitor to discharge to 0.100% of its full value after discharge begins.

Given, V=100% and V'=0.100%It is known that the equation for the capacitor voltage with time during discharge is given by;V = V0e-t/RCSubstituting for the final and initial voltages we have,0.100% V0 = V0e-t/RC

Taking the natural logarithm of both sides,ln(0.001) = -t/RCln(0.001) = -t/1.2 x 10^3 x 2.2 x 10^-6t = 31.2 seconds (to the nearest whole number)Therefore, it will take approximately 31.2 seconds to reduce the voltage on the capacitor to 0.100% of its full value once discharge begins.

(c) If the capacitor is charged to a voltage V0 through a 133Ω resistance, calculate the time it takes to rise to 0.865V0 (this is about two time constants).It is known that the equation for the capacitor voltage with time during charging is given by;V = V0(1 - e-t/RC)

We are required to find the time it takes for the voltage across the capacitor to rise to 0.865V0, which is equivalent to a voltage difference of 0.135V0 from the initial voltage.

Therefore, substituting for the final and initial voltages we have,0.865V0 = V0(1 - e-2T/RC)Rearranging,1 - 0.865 = e-2T/RCln(0.135) = -2T/RCt = 2T = 2 x 1.2 x 10^3 x 2.2 x 10^-6 x ln(0.135)t = 26.4 seconds (to the nearest whole number) Therefore, it takes approximately 26.4 seconds to rise to 0.865V0.

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A 3.0 kg puck slides on frictionless surface at 0.40 m/s and strikes a 4.0 kg puck at rest. The first puck moves off at 0.30 m/s at an angle +35 degrees from the incident direction. What is the velocity of the 4.0 kg puck after the impact?

Answers

After the impact, the 4.0 kg puck acquires a velocity of approximately 0.75 m/s in the opposite direction of the incident puck's original motion.

To solve this problem, we can apply the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. The momentum of an object is calculated by multiplying its mass by its velocity.

Before the collision, the total momentum is given by:

Initial momentum = (mass of first puck * velocity of first puck) + (mass of second puck * velocity of second puck)

= (3.0 kg * 0.40 m/s) + (4.0 kg * 0 m/s) [since the second puck is initially at rest]

= 1.2 kg m/s

After the collision, the total momentum is given by:

Final momentum = (mass of first puck * velocity of first puck after collision) + (mass of second puck * velocity of second puck after collision)

= (3.0 kg * 0.30 m/s * cos(35 degrees)) + (4.0 kg * velocity of second puck after collision)

Since the first puck moves off at an angle, we need to use the cosine of the angle to calculate the horizontal component of its velocity.

Solving the equation, we find that the velocity of the 4.0 kg puck after the impact is approximately 0.75 m/s.

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A 1.60-m long steel piano wire has a diameter of 0.20 cm. What is the needed tension force in the wire for it to stretch at a length of 0.25 cm? (Continuation) What is the amount of force that could break this wire? The ultimate strength of steel is 500 x10 Pa. What is the elongation length of the wire the moment it breaks?

Answers

To calculate the tension force required to stretch a steel piano wire, we can use Hooke's Law and the formula for the cross-sectional area of a wire. The force that could break the wire can be determined using the ultimate strength of steel. The elongation length of the wire at the moment it breaks can be found using the equation for strain.

To find the tension force required to stretch the piano wire by a certain length, we can use Hooke's Law, which states that the force applied to a spring or elastic material is proportional to the displacement or change in length. The formula for Hooke's Law is F = kΔL, where F is the tension force, k is the spring constant (related to the wire's Young's modulus and cross-sectional area), and ΔL is the change in length.

First, we need to find the cross-sectional area of the wire using its diameter. The formula for the area of a circle is A = πr², where r is the radius. In this case, the diameter is given, so we can divide it by 2 to find the radius.

Once we have the cross-sectional area, we can calculate the spring constant using Young's modulus, which is a property of the material. The spring constant is given by k = (YA) / L, where Y is the Young's modulus, A is the cross-sectional area, and L is the original length of the wire.

To calculate the force that could break the wire, we use the ultimate strength of steel, which is a measure of the maximum stress a material can withstand without breaking. The force is given by F_break = A * ultimate strength.

Finally, to find the elongation length at the moment the wire breaks, we can use the equation for strain: ΔL / L = F_break / (A * Y), where ΔL is the elongation length, L is the original length, F_break is the force that could break the wire, A is the cross-sectional area, and Y is the Young's modulus.

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A loop of wire with velocity 3 m/s moves through a magnetic field whose strength increases with distance at a rate of 5T/m. If the loop has area 0.75 m² and internal resistance 5 Ω, what is the current in the wire?
A. I=3 A
B. I=56A
C. I=11.25 A
D. I=2.25A

Answers

The current in the wire is option is A, I = 3A.

The rate of increase of the magnetic field is 5 T/m and the velocity of the wire is 3 m/s.

Therefore, the change in the magnetic field per unit time, that is, the emf induced in the wire is;

emf = Bvl

where

B is the magnetic field,

v is the velocity,

l is the length of the wire, in this case, the length of the wire is equal to the perimeter of the loop.

The area of the loop is 0.75 m²;

therefore, the perimeter is;

P = √(4 × 0.75 m² / π) = 0.977m

Substituting the values given;

emf = (5 T/m × 3.08 m) × 3 m/s = 14.655 V

The current in the wire is given by;

I = emf / R

where

R is the internal resistance of the wire, in this case, it is 5 Ω.

Substituting the values in the equation,

I = 14.655 V / 5 Ω = 2.931 A = 3A(approx)

Therefore, the correct option is A. I = 3A.

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Part C
Just like in the diagram, when Earth was primarily liquid, it separated into layers. What prediction can you make about the
densities of Earth's different layers?

Answers

When the Earth was primarily liquid, it separated into layers. The density of Earth's different layers may be predicted. For instance, it is assumed that the outermost layer, or crust, is less dense than the inner layers.

The Earth's crust is mostly composed of silicates (such as quartz, feldspar, and mica) and rocks, which are less dense than the mantle, core, or outer core.

The mantle is composed of solid rock, which is denser than the Earth's crust.

The core is the most dense layer, and it is composed of a liquid outer core and a solid inner core.

Most of the Earth's layers are composed of different types of rock and minerals.

The layers were formed from the molten material that cooled and solidified.

The Earth's layers are divided into four groups, or spheres, that represent different levels of density.

The lithosphere is the outermost layer, which includes the crust and upper mantle.

The asthenosphere is the soft layer beneath the lithosphere.

The mantle is a solid layer that surrounds the core.

The core is the Earth's central layer, consisting of a liquid outer core and a solid inner core.

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A capacitor is a device used to store electric charge which allows it to be used in digital memory. a) Explain how a capacitor functions. b) What is the impact of using a dielectric in a capacitor? c) Define what is meant by electric potential energy in terms of a positively charge particle in a uniform electric field. d) How does electric potential energy relate to the idea of voltage?

Answers

a) When a voltage is applied, electrons accumulate on one plate and positive charge accumulates on the other, creating an electric field between the plates. b) The use of a dielectric in a capacitor increases its capacitance by reducing the electric field between the plates. c) Electric potential energy refers to the energy possessed by a positively charged particle in a uniform electric field. d)The potential energy of a charged particle in an electric field is proportional to the voltage across the field. As the voltage increases, the electric potential energy of the system increases, and vice versa.

a) A capacitor consists of two conductive plates separated by a dielectric material. When a voltage is applied across the plates, one plate accumulates an excess of electrons, becoming negatively charged, while the other plate accumulates a deficit of electrons, becoming positively charged. This creates an electric field between the plates. The dielectric material between the plates serves to increase the capacitance of the capacitor by reducing the electric field and allowing for a greater charge storage capacity.

b) The use of a dielectric in a capacitor has a significant impact on its performance. The dielectric material, often an insulating substance such as ceramic or plastic, increases the capacitance of the capacitor. It does this by reducing the electric field between the plates, which in turn reduces the voltage required to maintain a certain charge. The dielectric material has a high dielectric constant, which indicates its ability to store electrical energy. By increasing the dielectric constant, the charge storage capacity of the capacitor increases, making it more efficient in storing and releasing electric charge.

c) Electric potential energy refers to the energy possessed by a positively charged particle in a uniform electric field. When a positive charge is placed in an electric field, it experiences a force in the direction opposite to the field. To move the charge against this force, work must be done. This work is stored as potential energy in the system. The electric potential energy is directly proportional to the magnitude of the charge, the electric field strength, and the distance the charge is moved against the field.

d) Electric potential energy is closely related to the concept of voltage. Voltage is a measure of the electric potential difference between two points in an electric field. It represents the amount of work done per unit charge in moving a charge between those two points. The potential energy of a charged particle in an electric field is directly proportional to the voltage across the field. As the voltage increases, the potential energy of the system also increases. Therefore, voltage can be seen as a measure of the electric potential energy difference between two points in an electric field.

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A star spans a parallax angle θ = 2 arcsecond when seen on Earth (6 months spans 2θ). Its distance is _____ light years from us.

Answers

A star spans a parallax angle θ = 2 arcsecond when seen on Earth (6 months spans 2θ). Its distance is 0.00000954 light years from us.

Parallax is a method used to measure the distance to nearby stars. The distance to the star is 0.00000954 light years, or 9.54 x 10^-6 light years, which was calculated using the parallax angle of 2 arcseconds observed on Earth. The parallax angle θ of a star is related to its distance d from Earth by the equation:

d = 1 / p

where p is the parallax in arcseconds.

In this problem, we are given that the star spans a parallax angle of 2 arcseconds when seen on Earth. Therefore, the distance to the star is:

d = 1 / (2 arcseconds) = 1 / 0.00055556 radians = 1800 radians

To convert this distance to light years, we need to divide by the speed of light, which is approximately 299,792,458 meters per second. Using the fact that there are approximately 31,536,000 seconds in a year, we get:

d = (1800 radians) / (299,792,458 meters/second × 31,536,000 seconds/year)

d = 0.00000954 light years

Therefore, the star is approximately 0.00000954 light years, or 9.54 × 10^-6 light years, away from us.

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Thin Lenses: A concave lens will O focalize light rays O reticulate light rays diverge light rays converge light rays

Answers

A concave lens will diverge light rays.

A concave lens is a thin lens that is thinner at the center than at the edges. When light rays pass through a concave lens, they are refracted or bent away from the principal axis of the lens. This bending of light causes the light rays to diverge or spread apart.

Unlike a convex lens, which converges light rays to a focal point, a concave lens disperses light rays. The diverging effect of a concave lens is due to the fact that the center of the lens is thinner than the edges, causing the light rays to bend away from each other.

This phenomenon is known as negative or diverging refraction. As a result, parallel light rays passing through a concave lens will spread out and appear to originate from a virtual point on the same side of the lens as the object. This point is called the virtual focal point.

The ability of a concave lens to diverge light rays makes it useful in correcting certain vision problems. For example, concave lenses are commonly used to correct nearsightedness (myopia), where the light rays converge before reaching the retina.

By adding a concave lens in front of the eye, the light rays are spread out, allowing them to focus properly on the retina.

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3.A ball of mass 0.8 Kg is dragged in the upward direction on an
inclined plane.Calculate the potential energy gained by this ball
at a height of the wedge of 0.2 meter.
please help. thank u

Answers

The potential energy gained by the ball at a height of wedge of 0.2 meter is 1.57 Joules.

What is potential energy?

Potential energy is the energy gained by the object by virtue of it's position or configuration.

For example water water stored in a dam or a bend scale certainly has some potential energy.  

The potential energy gained by the ball of mass 0.8 Kg at a height of the wedge of 0.2 meter can be calculated using the formula given below:

Potential energy (P.E) = mass of object x acceleration due to gravity x height of the object

PE= mgh

Here, m = 0.8 kg, g = 9.8 m/s² and h = 0.2 m.

So, substituting these values in the above formula, we get the potential energy gained by the ball at a height of the wedge of 0.2 meter.

PE = 0.8 x 9.8 x 0.2

PE = 1.568 Joules

Therefore, the potential energy gained by the ball of mass 0.8 Kg at a height of the wedge of 0.2 meter is 1.568 Joules.

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Liquid isobutane is throttled through a valve from an initial state of 360 K and 4000 kPa to a final pressure of 2000 kPa. Estimate the temperature change and the
entropy change of the isobutane. The specific heat of liquid isobutane at 360 K is
2.78 J·g−1·°C−1. Estimates of V and β may be found from Eq. (3.68).
can you please please please explain step by stepVsat=VcZ(1-T)2/7

Answers

In this problem, we are given that liquid isobutane is throttled through a valve from an initial state of 360 K and 4000 kPa to a final pressure of 2000 kPa. We have to estimate the temperature change and the entropy change of the isobutane. The specific heat of liquid isobutane at 360 K is 2.78 J·g−1·°C−1.

From the given problem, we have initial and final pressure. Also, specific heat is given. From the following equation,

Δh = Cp ΔT

Here, Δh represents the enthalpy change, Cp represents the specific heat at constant pressure, and ΔT represents the temperature change.

We can find ΔT by dividing the change in enthalpy by the specific heat. Here, enthalpy change can be found using the following equation,

h2 - h1 = V(P2 - P1)

where, V is the specific volume of the liquid, and P1 and P2 are the initial and final pressures, respectively. We can estimate V using the following equation,

V sat = VcZ(1 - Tc/T)^(2/7)

Here, V sat is the saturation volume, Vc is the critical volume, Tc is the critical temperature, T is the temperature at which we want to estimate V, and Z is the compressibility factor.

We are also required to estimate the entropy change. The entropy change for a throttling process is given by,

Δs = Cp ln(P1/P2)

Therefore, we can estimate the temperature change and entropy change using the equations above.

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Compare and contrast series and parallel circuits; Include voltage and current distribution, effective resistance;

Answers

Series and parallel circuits are two common arrangements of electrical components in a circuit. Here is a comparison and contrast between the two:

Voltage and Current Distribution:

In a series circuit, the same current flows through each component. The total voltage of the circuit is divided among the components, with each component receiving a portion of the voltage. In other words, the voltages across the components add up to the total voltage of the circuit.

In a parallel circuit, the voltage across each component is the same. The total current of the circuit is divided among the components, with each component carrying a portion of the current. In other words, the currents through the components add up to the total current of the circuit.

Effective Resistance:

In a series circuit, the effective resistance (total resistance) is the sum of the individual resistances. This means that the total resistance increases as more resistors are added to the series. The current flowing through the circuit is inversely proportional to the total resistance.

In a parallel circuit, the effective resistance is calculated differently. The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. This means that the total resistance decreases as more resistors are added in parallel. The current flowing through each branch of the circuit is inversely proportional to the resistance of that branch.

Comparison:

- In series circuits, components are connected one after another, forming a single path for current flow. In parallel circuits, components are connected side by side, providing multiple paths for current flow.

- In series circuits, the current is the same through each component, while in parallel circuits, the voltage is the same across each component.

- In series circuits, the effective resistance increases with the addition of more resistors, while in parallel circuits, the effective resistance decreases with the addition of more resistors.

Contrast:

- Series circuits have a single path for current flow, while parallel circuits have multiple paths.

- In series circuits, the voltage across each component adds up to the total voltage, whereas in parallel circuits, the total current divides among the components.

- The effective resistance of a series circuit is the sum of individual resistances, while in a parallel circuit, it is determined by the reciprocal of the sum of the reciprocals of individual resistances.

Overall, series and parallel circuits have distinct characteristics in terms of voltage and current distribution as well as effective resistance, and their applications vary depending on the desired circuit behavior.

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At dawn, with the Sun just rising in the east, you face the Sun and bend your head back to look straight up, and you examine the blue sky light with a Polaroid filter. (a) [2 points] Why is the light polarized? (b) (2 points) What is the direction of the electric field, east-west or north-south? Explain briefly why

Answers

a. Polarization is caused by the scattering of sunlight off air molecules in the Earth's atmosphere.

b. when you examine the blue sky light with a Polaroid filter, the direction of the electric field is North-South.

a. The electric fields of electromagnetic waves are caused by the vibration of charged particles. A polarized filter is able to block one direction of polarization while allowing the other direction to pass through. This happens because a polarizing filter is made up of a long chain of molecules oriented in one direction, which blocks light waves with electric fields oriented in a perpendicular direction.

The polarization of sunlight is due to the scattering of light off air molecules. This scattering causes light waves with electric fields oriented in a perpendicular direction to the Sun to be polarized. The electric fields of light waves in the blue part of the spectrum are oriented in a north-south direction, while the electric fields of light waves in the red part of the spectrum are oriented in an east-west direction.

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A single-slit diffraction pattern is formed when light of λ = 740.0 nm is passed through a narrow slit. The pattern is viewed on a screen placed one meter from the slit. What is the width of the slit (mm) if the width of the central maximum is 2.25 cm?

Answers

The width of the slit can be calculated by using the formula for single-slit diffraction. In this case, the width of the central maximum is given as 2.25 cm, and the wavelength of the light is 740.0 nm. The width of the slit is 0.7400 * 10^-3 mm.

By substituting these values into the formula, the width of the slit can be determined.

The single-slit diffraction pattern can be characterized by the equation:

sin(θ) = m * λ / w

where θ is the angle of diffraction, m is the order of the maximum (for the central maximum, m = 0), λ is the wavelength of the light, and w is the width of the slit.

In this case, the width of the central maximum is given as 2.25 cm. To convert this to meters, we divide by 100: 2.25 cm = 0.0225 m. The wavelength of the light is given as 740.0 nm, which is already in meters.

For the central maximum (m = 0), the angle of diffraction is zero. Therefore, sin(θ) = 0, and the equation becomes:

0 = 0 * λ / w

Simplifying the equation, we find that the width of the slit is equal to the wavelength:

w = λ

Substituting the given wavelength, we have:

w = 740.0 nm = 0.7400 μm = 0.7400 * 10^-3 mm

Therefore, the width of the slit is 0.7400 * 10^-3 mm.

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(b) Two charged concentric spherical shells have radi 5.0 cm and 10 cm. The charge on the inner shell is 5.0 ng, and that on the outer shell is-20 nC. In order to calculate the electric field at a distance of 20 cm from the centre of the spheres, an appropriate Gaussian surface is A sphere with a radius of 20 cm A sphere with a radius of 10 cm a A cylinder with a radius of 20 cm A sphere with a radius of 70 cm (1) The total enclosed charge is 3.0 nc 70 nc -20 nc 5.0 nc (i) Calculate the electric field in Newtons per Coulomb at 20 cm

Answers

Answer: the electric field at a distance of 20 cm from the center of the spheres is 1.8 × 10^3 N/C.

The appropriate Gaussian surface to calculate the electric field at a distance of 20 cm from the center of the spheres is a sphere with a radius of 20 cm.

(1) The total enclosed charge is -20 nC + 5.0 ng. The total enclosed charge is

-20 nC + 5.0 ng =

-20 × 10^-9 C + 5.0 × 10^-9 C

= -15.0 × 10^-9 C.

(i) The electric field in Newtons per Coulomb at 20 cm. The electric field in N/C at a point at a distance r from the center of a spherical shell of radius R and charge q is given by the equation

E = {q(r)/4πε₀r³}.

E = Electric field in N/Cq. (r) = Total charge enclosed within the Gaussian surface which is -15.0 × 10^-9 C. ε₀ = Permittivity of free space = 8.854 × 10^-12 C²/N.m². r = distance from the center of the shell where the electric field is being calculated = 20 cm = 0.20 m.

For r > R₂, the electric field at a point outside a shell of charge q and radius R₂ is zero.

Hence, only the electric field due to the 5.0 cm inner shell will be considered. E = {q(r)/4πε₀r³}E = {5.0 × 10^-9 C/4π(8.854 × 10^-12 C²/N.m²)(0.20 m)³}E = 1.8 × 10^3 N/C.

Therefore, the electric field at a distance of 20 cm from the center of the spheres is 1.8 × 10^3 N/C.

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Suppose you measure the terminal voltage of a 3.280 V lithium cell having an internal resistance of 4.70 Ω by placing a 1.00 kΩ voltmeter across its terminals. (a) What current flows (in amps)? __________ A (b) Find the terminal voltage. _____________ V (c) To see how close the measured terminal voltage is to the emf, calculate their difference. __________ V

Answers

the current flows through the circuit is 0.697 A.

the terminal voltage is 6.55 V.

the difference between the measured terminal voltage and the emf is 3.25 V

The voltage of a 3.280 V lithium cell having an internal resistance of 4.70 Ω measured by placing a 1.00 kΩ voltmeter across its terminals. We have to find the current, terminal voltage, and the difference between the measured terminal voltage and the emf.

(a) The current flows can be calculated using Ohm's law which states that

V=IR

Where;

V = voltage = 3.280V

R = internal resistance = 4.70 Ω

I = current

Rearranging the above equation, we get

I = V / R

I = 3.280V / 4.70 Ω

I = 0.697 A

Therefore, the current flows through the circuit is 0.697 A.

(b) Now, we have to find the terminal voltage;

The voltage drop across the internal resistance of the lithium cell is;V

IR = IRV

IR = (0.697 A)(4.70 Ω)V

IR = 3.27 V

The total voltage across the terminals can be found by adding the voltage drop across the internal resistance to the voltage measured by the voltmeter.

V = Vmeasured + VIR

V = 3.280 V + 3.27 V

V = 6.55 V

Therefore, the terminal voltage is 6.55 V.

(c) The difference between the measured terminal voltage and the emf can be calculated as follows;

V - Vemf=IR

Where;

V = terminal voltage = 6.55 V

Vemf = voltage of the cell = 3.280

V= internal resistance = 4.70 Ω

I = current

Rearranging the above equation, we get;

Vemf = V - IR

Vemf = 6.55 V - (0.697 A)(4.70 Ω)

Vemf = 3.25 V

Therefore, the difference between the measured terminal voltage and the emf is 3.25 V.

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Part C
Now, to get numerical equations for x and y, you’ll need to know the initial values (at time t = 0) for some velocities and accelerations. On the Table below the video:

Select cm as the mass measurement set to display.
Click the Table label and check all x and y displacement and velocity data: x, y, vx, and vy. Then click Close.
Now rewrite the displacement equations from Part A and Part B above by substituting in the x and y velocity values from time t = 0 and also using the theoretical value of acceleration of gravity. Write them out below.

Answers

To rewrite the displacement equations from Part A and Part B, we'll substitute in the x and y velocity values from time t = 0 and use the theoretical value of acceleration due to gravity.

Displacement equations for x-axis (horizontal motion):

1. x = (vx)t

  where vx is the initial velocity in the x-direction.

Displacement equation for y-axis (vertical motion):

1. y = (vy)t + (1/2)(g)(t^2)

  where vy is the initial velocity in the y-direction and g is the acceleration due to gravity.

1. Start by selecting cm as the mass measurement set to display.

2. Click on the Table label and check all x and y displacement and velocity data: x, y, vx, and vy.

3. Click Close to save the changes.

4. Now, let's rewrite the displacement equations using the given values.

  - For the x-axis displacement, substitute the initial x-velocity value (vx) at time t = 0 into the equation: x = (vx)t.

  - For the y-axis displacement, substitute the initial y-velocity value (vy) at time t = 0 and the acceleration due to gravity (g) into the equation: y = (vy)t + (1/2)[tex](g)(t^2[/tex]).

Please note that the specific values for vx, vy, and g should be provided in the question or the given table. Make sure to substitute the correct values to obtain the numerical equations for x and y displacement.

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The smaller disk dropped onto a larger rotating one. (frame rate=30fps. Frames=36)(time 1.2 s). The large disk is made of dense plywood rotating on a low-friction bearing. The masses of the disks are: large disk: 2.85kg Radius of large disk = 0.3m small disk: 3.06 kg Radius of small disk= 0.18m
(1) Make measurements and calculations to determine the final speed of the two disk rotating together, and calculate the percent difference between your predicted value and the experimental value. Hint: The final velocity of the two-disk system should be measured when the two disks reach the same angular velocity. How can you tell when that happens?
(2) Determine the total angular momentum of the two-disk system after the smaller disk is dropped on the larger one. Calculate the percent difference: percent change=((L sys−L sys)​/L sys)×100
(3) Determine the total kinetic energy of the two-disk system before and after the collision. Calculate the percent difference between the two values.
(4) Compare the percent change in angular momentum of the system to the percent change in the rotational kinetic energy of the system. Explain the difference between these two values.

Answers

The final speed of the two-disk system can be determined by equating the angular momentum before and after the collision. The total angular  of the two-disk system after the smaller disk is dropped on the larger one is the sum of the individual angular momenta of the disks.

(1) The angular momentum is given by the product of the moment of inertia and the angular velocity. Since the system is initially at rest, the initial angular momentum is zero. When the two disks reach the same angular velocity, the final angular momentum is given by the sum of the individual angular momenta of the disks. By equating these two values, we can solve for the final angular velocity. The final linear speed can then be calculated by multiplying the final angular velocity with the radius of the combined disks. To determine when the disks have reached the same angular velocity, one can observe their motion visually and note when they appear to be rotating together smoothly.

(2) The angular momentum of a disk is given by the product of its moment of inertia and angular velocity. By adding the angular momenta of the large and small disks, we can calculate the total angular momentum of the system. The percent difference can be calculated by comparing this value to the initial angular momentum, which is zero since the system starts from rest.

(3) The total kinetic energy of the two-disk system before and after the collision can be calculated using the formulas for rotational kinetic energy. The rotational kinetic energy of a disk is given by half the product of its moment of inertia and the square of its angular velocity. By summing the rotational kinetic energies of the large and small disks, we can determine the initial and final kinetic energies of the system. The percent difference can be calculated by comparing these two values.

(4) The percent change in angular momentum of the system and the percent change in the rotational kinetic energy of the system may not be the same. This is because angular momentum depends on both the moment of inertia and the angular velocity, while rotational kinetic energy depends only on the moment of inertia and the square of the angular velocity. Therefore, changes in the angular velocity may not be directly proportional to changes in the rotational kinetic energy. The difference between these two values can arise due to factors such as the redistribution of mass and changes in the system's geometry during the collision.

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The output power of a 400/690 V, 50 Hz, Y-connected induction motor, shown below, is 15 kW. It runs at full load with a speed of 2940 RPM. Choose the correct statement: The motor's synchronous speed is 3000 RPM and its rated power is 30 HP. O The motor's synchronous speed is 2500 RPM at 50 Hz. O The motor has 2 poles and operates at a slip of 6%. o The motor torque at full load is 48.4 Nm O The motor has 4 poles and operates at a slip of 2%.

Answers

The correct statement is that the motor has 4 poles and operates at a slip of 2%. and the motor torque at full load is 48.4 Nm

Synchronous speed of induction motor The synchronous speed (N_s) of an induction motor is calculated using the below formula: N_s = (f/P) × 120 where, f is the frequency of the power supply applied P is the number of poles in the motor

From the above formula, we get the synchronous speed of the motor = (50/2) × 120 = 3000 RPM

The motor operates at a slip of 2%.

The speed of the motor is given by, Speed of motor (N) = Synchronous speed – Slip speed where Slip speed = (Slip × Synchronous speed) / 100

Now, Speed of motor (N) = 3000 – (2% × 3000) = 2940 RPM

Therefore, the motor has 4 poles. The rated power of the motor is given as 15 kW, which is equal to 20 HP (1 HP = 0.746 kW).

So, the motor's rated power is 20 HP.

The formula for calculating the motor torque is given by the below formula, T = (P × 60) / (2 × π × N) Where, P = Output power of the motor

N = Speed of the motor

Substituting the values we get, T = (15 × 60) / (2 × π × 2940) = 48.4 Nm

Therefore, the motor torque at full load is 48.4 Nm.

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The complete question is -

The output power of a 400/690 V, 50 Hz, Y-connected induction motor, shown below, is 15 kW. It runs at full load with a speed of 2940 RPM. Choose the correct statement:

o The motor's synchronous speed is 3000 RPM and its rated power is 30 HP.

O The motor torque at full load is 48.4 Nm O The motor has 4 poles and operates at a slip of 2%.

O The motor has 2 poles and operates at a slip of 6%.

O The motor's synchronous speed is 2500 RPM at 50 Hz.

A transformer is used to step down 160 V from a wall socket to 9.1 V for a radio. (a) If the primary winding has 600 turns, how many turns does the secondary winding have?_____ turns (b) If the radio operates at a current of 480 mA, what is the current (in mA) through the primary winding? ____mA

Answers

(a) If the primary winding has 600 turns, how many turns does the secondary winding have? 34 turns (b) If the radio operates at a current of 480 mA, what is the current (in mA) through the primary winding? 27.2 mA.

(a) Given that the primary winding has 600 turns and the voltage across the primary winding is 160 V, and the voltage across the secondary winding is 9.1 V, we can calculate the number of turns in the secondary winding (N2) as follows: Picture is given below.

Therefore, the secondary winding has approximately 34 turns.

(b)To find the current through the primary winding, we can use the current ratio equation:

[tex]\frac{I1}{I2}[/tex] = [tex]\frac{N2}{N1}[/tex]

where I1 and I2 re the currents through the primary and secondary windings respectively, and N1 and N2are the number of turns in the primary and secondary windings respectively.

Given that the current through the secondary winding (I2) is 480 mA, and the number of turns in the primary winding (N1) is 600, we can calculate the current through the primary winding (I1) as follows: Picture is given below.

Therefore, the current through the primary winding is approximately 27.2 mA.

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That is when the aliens shined light onto their double slit and shouted "Wahahaha, the pattern through this double slit has both double-slit and single-slit effects! You will be tempted to calculate the relationship between the slit width a and slit separation d! While you do that, we are going to attack you, hehehehe!!" They were right, as soon as you saw that the second diffraction minimum coincided with the 14th double-slit maximum, you couldn't think about anything else. What is the relationship between a (slit width) and d (slit separation)? 1 d = 14 a = Od = 7a Od = a/14 d = a/7

Answers

in the given scenario, the relationship between the slit width (a) and the slit separation (d) is determined to be d = a/7, based on the coincidence of the second diffraction minimum with the 14th double-slit maximum.

The double-slit experiment involves passing light through two parallel slits and observing the resulting interference pattern. The pattern consists of alternating bright and dark fringes. The bright fringes correspond to constructive interference, while the dark fringes correspond to destructive interference.

In this case, the second diffraction minimum coincides with the 14th double-slit maximum. The diffraction minimum occurs when the path lengths from the two slits to a particular point differ by half a wavelength, resulting in destructive interference.The double-slit maximum occurs when the path lengths are equal, leading to constructive interference.Since the second diffraction minimum corresponds to the 14th double-slit maximum, we can conclude that the path length difference for the second diffraction minimum is equal to 14 times the wavelength.

The path length difference can be expressed as d*sin(θ), where d is the slit separation and θ is the angle of deviation. For small angles, sin(θ) is approximately equal to θ in radians.Therefore, we have d*sin(θ) = 14λ, where λ is the wavelength of light.Assuming the angle of deviation is small, we can approximate sin(θ) as θ.

Thus, we have d*θ = 14λ.For a small angle, θ can be related to a and d using the small angle approximation: θ ≈ a/d.Substituting this into the previous equation, we get d*(a/d) = 14λ.The d cancels out, resulting in a = 14λ.Therefore, the relationship between the slit width (a) and the slit separation (d) is d = a/7.

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Your friend is a new driver in your car practicing in an empty parking lot. She is driving clockwise in a large circle at a constan speed. Is the car traveling with a constant velocity or is it accelerating?: Since the car is changing direction as it travels around the circle, it has a centripetal acceleration and does not have a constant velocity. The car has a constant speed, so the velocity is constant and there is no acceleration.

Answers

Centripetal acceleration, which points towards the center of the circle, is responsible for this change in direction. Thus, while the car is traveling at a constant speed, it is still accelerating since the direction of its velocity is constantly changing.

The car has a centripetal acceleration and does not have a constant velocity. Although the car is traveling with a constant speed, it is still accelerating.What is acceleration?Acceleration refers to the rate of change of velocity. Acceleration may be either positive or negative. When an object speeds up, it has positive acceleration.

When an object slows down, it has negative acceleration, which is also known as deceleration. When an object changes direction, it experiences acceleration.A car driving in a circle at a constant speed is an example of uniform circular motion.

The car's direction is constantly changing since it is moving in a circular path. As a result, the car's velocity is constantly changing even if its speed is constant.

Centripetal acceleration, which points towards the center of the circle, is responsible for this change in direction.

Thus, while the car is traveling at a constant speed, it is still accelerating since the direction of its velocity is constantly changing.

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A heat pump with a C.O.P equal to 2.4, consumes 2700 kJ of electrical energy during its operating period. During this operating time, 1)how much heat was transferred to the high-temperature tank?
2)How much heat has been moved from the low-temperature tank?

Answers

Therefore, the amount of heat transferred to the high-temperature tank is 6480 kJ and the amount of heat moved from the low-temperature tank is 3780 kJ.

1)The heat transferred to the high temperature tank can be found out using the given equationQh = COP * WWhere,Qh = Heat transferred to the high-temperature tankCOP = Coefficient of PerformanceW = Work done by the system

Substituting the given values, we haveQh = 2.4 * 2700kJQh = 6480 kJ2)The heat moved from the low-temperature tank can be found out using the formulaQl = Qh - WWhere,Ql = Heat moved from the low-temperature tankQ

h = Heat transferred to the high-temperature tankW = Work done by the systemSubstituting the values from part 1 and work done from the given question, we haveQl = 6480 kJ - 2700 kJQl = 3780 kJ

Therefore, the amount of heat transferred to the high-temperature tank is 6480 kJ and the amount of heat moved from the low-temperature tank is 3780 kJ.

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Two crates, of mass m1m1 = 64 kgkg and m2m2 = 123 kgkg , are in contact and at rest on a horizontal surface. A 700 NNforce is exerted on the 64 kgkg crate.
I need help with question c and d
c) Repeat part A with the crates reversed.
d) Repeat part B with the crates reversed.
part a and b ---> If the coefficient of kinetic friction is 0.20, calculate the acceleration of the system. = 1.8 m/s^2
Calculate the force that each crate exerts on the other. = 460 N

Answers

part(c) Hence, the acceleration of the system is 3.74 m/s². part(d) Hence, the force that each crate exerts on the other is 119.2 N.

Part (c): If we reverse the crates, that is, if 123 kg mass crate comes in contact with 64 kg mass crate and a force of 700 N is applied on 123 kg crate,

Then the acceleration can be calculated as follows: We need to find the acceleration of the system, which can be calculated using the formula, Total force, F = ma

Where, F = 700 N (force applied on the system)m = m1 + m2 = 64 kg + 123 kg = 187 kg a = acceleration of the system

Hence, the acceleration of the system is 3.74 m/s²

Part (d): If we reverse the crates, then the force that each crate exerts on the other can be calculated as follows:

Let us assume that f is the force that each crate exerts on the other. Then, f is given by:

From the free-body diagram of the 64 kg crate, we have:fn1 = Normal force exerted by the surface on the 64 kg cratefr1 = force of friction acting on the 64 kg crate due to contact with the surface

From the free-body diagram of the 123 kg crate, we have:fn2 = Normal force exerted by the surface on the 123 kg cratefr2 = force of friction acting on the 123 kg crate due to contact with the surface.

Then we have the equations: For the 64 kg crate,fn1 - f = m1 * a ... (1)where a is the acceleration of the system.

As we have calculated a in part (a), we can substitute the value of a into the equation and solve for f.

For the 123 kg crate,fn2 + f = m2 * a ... (2)From equation (2), we have, f = (m2 * a - fn2)

From equation (1), we have,fn1 - f = m1 * afn1 - f = m1 * 1.8fn1 - f = 64 * 1.8fn1 - f = 115.2fn1 = 115.2 + ff = fn1/2 + fn1/2 - m2 * a + fn2/2f = 230.4/2 - (123 * 3.74) + 580.8/2

Hence, the force that each crate exerts on the other is 119.2 N.

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A wheel rotates with a constant angular acceleration of 3.50rad/s 2
. A) If the angular speed of the wheel is 2.00rad/s at t i

=0, through what angular displacement does the wheel rotate in 2.00 s ? B) What is the angular speed of the wheel at t=2.00 s ?

Answers

A wheel has a constant angular acceleration of 3.50 rad/s². The wheel rotates through an angular displacement of 8.00 radians in 2.00 seconds. The angular speed is ω = 8.00 rad/s.

A) To calculate the angular displacement of the wheel in 2.00 seconds, we can use the formula θ = ωi * t + (1/2) * α * t², where θ is the angular displacement, ωi is the initial angular speed, α is the angular acceleration, and t is the time. Substituting the given values into the formula, we have θ = (2.00 rad/s) * (2.00 s) + (1/2) * (3.50 rad/s²) * (2.00 s)². Evaluating this expression gives θ = 8.00 rad. Therefore, the wheel rotates through an angular displacement of 8.00 radians in 2.00 seconds.

B) To find the angular speed of the wheel at t = 2.00 seconds, we can use the formula ω = ωi + α * t, where ω is the angular speed at a given time. Substituting the values into the formula, we have ω = (2.00 rad/s) + (3.50 rad/s²) * (2.00 s). Calculating this expression gives ω = 8.00 rad/s.

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The origins of two frames coincide at t = t' = 0 and the relative speed is 0.996c. Two micrometeorites collide at coordinates x = 101 km and t = 157 μs according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S’? (a) Number ___________ Units _______________
(b) Number ___________ Units _______________

Answers

The origins of two frames coincide at t = t' = 0 and the relative speed is 0.996c.

Two micrometeorites collide at coordinates x = 101 km and t = 157 μs according to an observer in frame S. We need to find the spatial and temporal coordinate of the collision according to an observer in frame S'.

x = 101 km, t = 157 μs

According to the observer in frame S', the relative velocity of frame S with respect to frame S' is u = v = 0.996c.

Let us apply the Lorentz transformation to the given values.

Lorentz transformation of length is given by, L' = L-√(1-u^2/c^2) Here, L = 101 km and u = 0.996c. We know that, c = 3 × 10^8 m/s.

Lorentz transformation of time is given by, T' = T-uX*c^2√(1-u^2/c^2)

Here, T = 157 μs, X = 101 km and u = 0.996c. We know that, c = 3 × 10^8 m/s.

Now, substituting the values in the above equations: L'=33.89 km

Hence, the spatial coordinate of the collision according to an observer in frame S' is 33.89 km.

The temporal coordinate of the collision according to an observer in frame S' is given by, T' = T-uX*c^2√1-u^2*c^2

Substituting the values of T, X and u, we get T' = -92.14μs

Hence, the temporal coordinate of the collision according to an observer in frame S' is -92.14 μs.

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A long straight wire carries a current of 5 A. What is the magnetic field a distance 5 mm from the wire? 1. 2.0 x 10-7 T B) 2.0 × 10-¹ T C) 6.3 x 10-¹ T D) 6.3 x 10-7 T

Answers

The magnetic field generated by a long straight wire carrying a current of 5 A at a distance of 5 mm from the wire is [tex]2.0 * 10^-^7[/tex] T.

According to Ampere's law, the magnetic field around a long straight wire is inversely proportional to the distance from the wire. The formula to calculate the magnetic field produced by a current-carrying wire is given by

[tex]B = (\mu_0 * I) / (2\pi * r)[/tex]

where B is the magnetic field, μ₀ is the permeability of free space[tex](4\pi * 10^-^7 T.m/A)[/tex], I is current, and r is the distance from the wire.

Plugging in the values,

[tex]B = (4\pi * 10^-^7 T.m/A * 5 A) / (2\pi * 0.005 m),[/tex]

which simplifies to:

[tex]B = 2.0 * 10^-^7 T[/tex].

Therefore, the magnetic field at a distance of 5 mm from the wire is [tex]2.0 * 10^-^7 T[/tex].

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A ²²Na source is labeled 1.50 mci, but its present activity is found to be 1.39 x 10⁷ Bq. (a) What is the present activity in mci? mci (b) How long ago (in y) did it actually have a 1.50 mci activity?

Answers

The present activity in mCi is 3.75 x 10⁵ mCi. It has 1.50 mci activity from 27.19 years.

A ²²Na source is labeled 1.50 mCi, but its present activity is found to be 1.39 x 10⁷ Bq.

(a) Present activity in mCi:

1 mCi = 37 MBq

So, 1.39 x 10⁷ Bq = 1.39 x 10⁷/37

mCi= 3.75 x 10⁵ mCi.

(b) Decay equation: A = A₀e⁻ᵦᵗwhere, A₀ = initial activity, A = present activity, t = time, and β = decay constant or disintegration constant.

Radioactive decay is first-order, so its decay constant is given by the equation:

β = 0.693/T₁/₂

where, T₁/₂ = half-life of ²²Na.

Half-life of ²²Na is 2.6 years.

So,

β = 0.693/2.6 = 0.2666 year⁻¹.

Using the decay equation:

A₀ = A/e⁻ᵦᵗ

A₀ = 1.50 mCi, A = 3.75 x 10⁵ mCi, and β = 0.2666 year⁻¹.

Substituting these values in the above equation and solving for t, we get:

t = [ln (A₀/A)]/β= [ln (1.50/3.75 x 10⁵)]/0.2666

= 27.19 years

Therefore, the ²²Na source had a 1.50 mCi activity 27.19 years ago.

Present activity in mCi = 3.75 x 10⁵ mCi

It has 1.50 mci activity from 27.19 years.

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An object is placed 45 cm to the left of a converging lens of focal length with a magnitude of 25 cm. Then a diverging lens of focal length of magnitude 15 cm is placed 35 cm to the right of this lens. Where does the final image form for this combination? Please give answer in cm Real or virtual?

Answers

Location of the final image: 27.38 cm to the right of the lens combination

Nature of the final image: Real. To determine the location and nature of the final image formed by the combination of the lenses, we can use the lens formula and the concept of lens combinations.

The lens formula for a single lens is given by:

1/f = 1/do + 1/di

Where:

f = focal length of the lens

do = object distance from the lens

di = image distance from the lens

For the converging lens:

f1 = 25 cm

do1 = -45 cm (since the object is placed to the left of the lens)

Using the lens formula for the converging lens:

1/25 = 1/-45 + 1/di1

Simplifying the equation, we find the image distance di1 for the converging lens:

di1 = 16.67 cm

Now, we consider the diverging lens:

f2 = -15 cm (since it is a diverging lens)

do2 = 35 cm (the object distance from the diverging lens)

Using the lens formula for the diverging lens:

1/-15 = 1/35 + 1/di2

Simplifying the equation, we find the image distance di2 for the diverging lens:

di2 = -10.71 cm

To find the final image distance, we need to consider the combination of the lenses. Since the diverging lens has a negative focal length, we consider it as a virtual object for the converging lens.

The final image distance di_final is given by:

di_final = di1 - do2

di_final = 16.67 - (-10.71)

di_final = 27.38 cm

Since the final image distance is positive, the image is real and formed on the same side as the object. Therefore, the final image forms 27.38 cm to the right of the lens combination.

The answer is:

Location of the final image: 27.38 cm to the right of the lens combination

Nature of the final image: Real

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A single-turn square loop carries a current of 16 A. The loop is 15 cm on a side and has a mass of 3.6×10 −2
kg - initially the loop lies flat on a horizontal tabletop. When a horizontal magnetic field is turned on, it is found that only one side of the loop experiences an upward force. Part A Find the minimum magnetic field, B min ​
, necessary to start lipping the loop up from the table. Express your answer using two significant figures. Researchers have tracked the head and body movements of several flying insects, including blowllies, hover fles, and honeybees. They attach lightweight, fexible wires to a small metai coli on the insect's head, and another-on its thorax, and then allow it to fly in a stationary magnetic field. As the coils move through the feld, they experience induced emts that can be analyzed by computer to determine the corresponding orientation of the head and thorax. Suppose the fly turns through an angle of 90 in 31 ms. The coll has 89 turns of wire and a diameter of 2.2 mm. The fly is immersed in a magnetic feld of magnitude 0.16 m T. Part A If the magnetic flux through one of the coils on the insect goes from a maximum to zero during this maneuver find the magnitude of the induced emf. Express your answer using two significant figures.

Answers

For the loop, the minimum magnetic field required to lift it from the table is approximately 0.24 T.

As for the flying insect, the magnitude of the induced emf in the coil due to a change in magnetic flux is approximately 0.29 mV.  For the square loop, we equate the magnetic force with the gravitational force. Magnetic force is given by BIL where B is the magnetic field, I is the current, and L is the length of the side. Gravitational force is mg, where m is mass and g is gravitational acceleration. Setting BIL=mg and solving for B gives us the minimum magnetic field. For the insect, the change in magnetic flux through the coil induces an emf according to Faraday's law, given by ΔΦ/Δt = N*emf, where N is the number of turns and Δt is the time taken. Solving for emf provides the induced voltage.

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