The magnetic field strength at a location on the axis of the coil, situated 0.70 m away from the center, is 2.0 × 10-4 T. At a distance of 0.70 m from the center of the coil, the field magnitude decreases to 1/8 of its value at the center.
(a) Here, the coil consists of 50 circular loops of radius r = 0.50 m and carries a current of I = 4.0 A. We need to find the magnetic field B at a point along the axis of the coil, 0.70 m from the center. The magnetic field at a point on the axis of a circular loop can be given by the formula:
[tex]$$B=\frac{\mu_0NI}{2r}$$[/tex] Where,
[tex]$$\mu_0 = 4\pi × 10^{-7} \ \mathrm{Tm/A}$$[/tex] is the permeability of free space.N is the number of turns in the coil. Here, N = 50. The radius of each circular loop in the coil is 0.50 m, and the current flowing through each turn is 4.0 A.
By plugging the provided values into the formula, we obtain the following result:
[tex]$$B=\frac{(4\pi × 10^{-7}\ \mathrm{Tm/A}) × 50 × 4.0\ \mathrm{A}}{2 × 0.50\ \mathrm{m}}$$[/tex]
[tex]$$\Rightarrow B = 2.0 × 10^{-4}\ \mathrm{T}$$[/tex]
Therefore, the magnetic field at a point along the axis of the coil, 0.70 m from the center is 2.0 × 10-4 T.
(b) Along the axis, the magnetic field of a coil falls off as the inverse square of the distance from the center of the coil. Let the distance of this point from the center be x meters. Therefore, the field at this point is given by:
[tex]$$\frac{B_0}{8}=\frac{\mu_0NI}{2\sqrt{x^2+r^2}}$$[/tex]
Here, B0 is the field at the center of the coil. From part (a), we know that,
[tex]$$B_0=\frac{\mu_0NI}{2r}$$[/tex]
[tex]$$\Rightarrow B_0=\frac{(4\pi × 10^{-7}\ \mathrm{Tm/A}) × 50 × 4.0\ \mathrm{A}}{2 × 0.50\ \mathrm{m}}$$[/tex]
[tex]$$\Rightarrow B_0 = 2.0 × 10^{-4}\ \mathrm{T}$$[/tex]
Substituting the values of B0 and I in the above equation and solving for x, we get:
[tex]$$\frac{2.0 × 10^{-4}\ \mathrm{T}}{8}=\frac{(4\pi × 10^{-7}\ \mathrm{Tm/A}) × 50 × 4.0\ \mathrm{A}}{2\sqrt{x^2+0.50^2\ \mathrm{m^2}}}$$[/tex]
[tex]$$\Rightarrow 2.5 × 10^{-5}\ \mathrm{T}=\frac{(4\pi × 10^{-7}\ \mathrm{Tm/A}) × 50 × 4.0\ \mathrm{A}}{\sqrt{x^2+0.50^2\ \mathrm{m^2}}}$$[/tex]
Solving for x, we get:
[tex]$$x=\sqrt{\frac{(4\pi × 10^{-7}\ \mathrm{Tm/A}) × 50 × 4.0\ \mathrm{A}}{2.5 × 10^{-5}\ \mathrm{T}}^2-0.50^2\ \mathrm{m^2}}$$[/tex]
[tex]$$\Rightarrow x = 0.70\ \mathrm{m}$$[/tex]
Therefore, the distance from the center of the coil at which the field magnitude is 1/8 as great as it is at the center is 0.70 m.
Learn more about magnetic field at: https://brainly.com/question/7645789
#SPJ11
Suppose 435 mL of Ne gas at 21 °C and 1. 09 atm, and 456 mL of SF6 at 25 °C and 0. 89 atm are put into a 325 mL flask at 30. 2 °C (a) What will be the total pressure in the flask? (b) What is the mole fraction of for each of the gases in the flask?
(a) To determine the total pressure in the flask, we need to consider the partial pressures of each gas present and add them together.
Using the ideal gas law, we can calculate the partial pressure of each gas:
PV = nRT
For Ne gas:
P₁V₁ = n₁RT
P₁ = (n₁/V₁)RT
For SF6 gas:
P₂V₂ = n₂RT
P₂ = (n₂/V₂)RT
To find the total pressure, we add the partial pressures:
P_total = P₁ + P₂
(b) The mole fraction (χ) of each gas can be calculated using the formula:
χ = moles of gas / total moles of gas
To find the moles of each gas, we use the ideal gas law rearranged:
n = PV / RT
Now, let's calculate the values.
Given:
Volume of Ne gas (V₁) = 435 mL = 0.435 L
Temperature of Ne gas (T₁) = 21 °C = 294 K
Pressure of Ne gas (P₁) = 1.09 atm
Volume of SF6 gas (V₂) = 456 mL = 0.456 L
Temperature of SF6 gas (T₂) = 25 °C = 298 K
Pressure of SF6 gas (P₂) = 0.89 atm
Volume of flask (V_total) = 325 mL = 0.325 L
Temperature of flask (T_total) = 30.2 °C = 303.2 K
Gas constant (R) = 0.0821 L·atm/(K·mol)
(a) To calculate the total pressure:
P₁ = (n₁/V₁)RT₁
P₁ = (PV₁/RT₁)
P₂ = (n₂/V₂)RT₂
P₂ = (PV₂/RT₂)
P_total = P₁ + P₂
(b) To calculate the mole fraction:
n₁ = P₁V_total / RT_total
n₂ = P₂V_total / RT_total
χ₁ = n₁ / (n₁ + n₂)
χ₂ = n₂ / (n₁ + n₂)
By plugging in the given values and performing the calculations, we can find the total pressure in the flask and the mole fraction of each gas.
Learn more about pressure here:-
brainly.com/question/30351725
#SPJ11
A conducting rod slides down between two frictionless vertical copper tracks at a constant speed of 4.0 m/5 perpendicular to a 0.57-T magnetic freld. The resistance of the rod and tracks is negligible. The rod maintains electrical contact with the tracks at all times and has a length of 1.8 m. A 0.74−Ω resistor is attached between the tops of the tracks. (a) What is the mass of the rod? (b) Find the change in the gravitational potential energy that occurs in a time of 0.205. (c) Find the electrical energy dissipated in the resistor in 0.20 s.
(a) the mass of the rod is [tex]$7.0 * 10^{-8}kg$[/tex].
(b) the potential energy change that occurs in [tex]$0.205s$[/tex] is [tex]$8.8 * 10^{-21}J$[/tex].
(c) the electrical energy dissipated in the resistor in [tex]$0.20s$[/tex] is [tex]$4.6 * 10^{-21}J$[/tex].
(a) Mass of the rod
The magnetic force acting on the rod causes a component of the gravitational force to be balanced. The component is that which pulls the rod downwards along the track. Therefore, the magnetic force acting on the rod is equal in magnitude but opposite in direction to the component of the gravitational force. Since the force is perpendicular to the velocity of the rod, it does not do any work. This implies that the kinetic energy of the rod is constant. This gives us the equation of motion of the rod as,
[tex]$mg\sinθ = BIl$[/tex]
[tex]$mg\sinθ = Bvq$[/tex]
Where the [tex]$v$[/tex] is the speed of the rod. Since the resistance of the rod and tracks is negligible, the potential difference between the points A and B is zero. This means that the electrical potential energy lost by the rod is equal to the gravitational potential energy gained by the rod. Therefore, [tex]$mgΔh = qvB$l[/tex]
where [tex]$\Delta h$[/tex] is the vertical distance through which the rod falls. Since [tex]$l=1.8m$, $\sinθ = \frac{1}{\sqrt{1+4/9}} ≈ 0.74$[/tex]. Thus,
[tex]$m = \frac{qBvl}{g\sin\theta}$[/tex]
Substituting the given values, we get,
[tex]$m = \frac{(1.6 * 10^{-19})(0.57)(4)(1.8)}{(9.8)(0.74)}$[/tex]
Therefore, the answer is [tex]$7.0 * 10^{-8}kg$[/tex].
Part (b)The potential energy lost by the rod when it drops a distance $\Delta h$ is given by,
[tex]$mg\delta h = qvB$l[/tex]
Thus, the potential energy change in a time of [tex]$0.205s$[/tex] is,
[tex]$\Delta U = mg\Deltah\frac{\Delta t}{v} = \frac{qB\Delta h}{v}$[/tex]
Substituting the given values, we get,
[tex]$\Delta U = \frac{(1.6 * 10^{-19})(0.57)(0.205)}{4}$[/tex]
Therefore, the answer is [tex]$8.8 * 10^{-21}J$[/tex].
Part (c)The electrical energy dissipated in the resistor is equal to the change in the potential energy of the rod, i.e. the gravitational potential energy lost by the rod. This is given by,
[tex]$\Delta U = mg\Delta h = qvB$l[/tex]
where [tex]$\Delta h[/tex]$ is the vertical distance through which the rod falls. Substituting the given values, we get,
[tex]$\Delta U = \frac{(1.6 * 10^{-19})(0.57)(0.20)}{4}$[/tex]
Therefore, the answer is [tex]$4.6 * 10^{-21}J$[/tex].
To learn more about potential energy change , refer:-
https://brainly.com/question/30657746
#SPJ11
(a) Sketch the relation between equivalent widths measured in a spectrum and the number of absorbing atoms. What is this relation called and what are the three main regimes and the physical explanation for these variations in the relation (2 points
The relation between equivalent widths measured in a spectrum and the number of absorbing atoms is known as the curve of growth. It exhibits three main regimes- linear regime, damping regime, and saturated regime.
The curve of growth describes the relationship between the equivalent widths measured in a spectrum and the number of absorbing atoms. It is a fundamental concept in spectroscopy. The curve of growth can be divided into three main regimes: the linear regime, the saturated regime, and the damping regime.
In the linear regime, the equivalent width of the spectral line is directly proportional to the number of absorbing atoms. As more absorbing atoms are added, the equivalent width increases linearly. In the saturated regime, adding more absorbing atoms does not result in a significant increase in the equivalent width. At this point, the spectral line becomes saturated, and the equivalent width plateaus.
In the damping regime, adding more absorbing atoms causes the equivalent width to decrease. This occurs because the line broadens due to collisions between the absorbing atoms. As the line broadens, the overall strength of the absorption decreases, resulting in a smaller equivalent width.
Understanding the curve of growth and its regimes is crucial for analyzing spectral data and determining the number of absorbing atoms in a system. By studying these variations, scientists can gain valuable insights into the physical properties of the absorbing medium.
Learn more about spectrum here:
https://brainly.com/question/31059971
#SPJ11
(a) No lens can focus light down to a perfect point because there will always be some diffraction. Estimate the size of the minimum spot of light that can be expected at the focus of a lens. Discuss the relationship among the focal length, the lens diameter, and the spot size [8] (b) Calculate the gain coefficient of a hypothetical laser having the following parameters: inversion density = 10¹7 cm-³, wavelength = 700 nm, linewidth = 1 nm, spontaneous emission lifetime = 10-4 s. Assume n≈ 1 for the refractive index of the amplifier medium. [8] (c) How long should the resonator be to provide the total gain of 4?
(a) This equation tells us that the spot size decreases with decreasing wavelength, increasing focal length, and decreasing lens diameter. (b) Therefore, the gain coefficient, G = 1.67 x 10-23(1/0.5)(1017-0) = 3.34 x 10-6 m-1. (c) Thus, the resonator should be L = ln(4)/2g to provide the total gain of 4.
(a) No lens can focus light down to a perfect point because there will always be some diffraction.
The minimum spot of light that can be expected at the focus of a lens can be estimated using the Rayleigh criterion, which states that the spot size is given by Δx = 1.22λf/D, where λ is the wavelength of light, f is the focal length of the lens, and D is the diameter of the lens aperture.
This equation tells us that the spot size decreases with decreasing wavelength, increasing focal length, and decreasing lens diameter.
(b) The gain coefficient of a hypothetical laser can be calculated using the formula G = σ(η/ηst)(N2-N1), where σ is the stimulated emission cross-section, η is the pump efficiency, ηst is the saturation efficiency, N2 is the population density of the upper laser level, and N1 is the population density of the lower laser level.
For a 3-level laser, the population density of the lower laser level can be assumed to be zero, so N1=0. Inversion density, N2 = 1017 cm-3, spontaneous emission lifetime, τsp = 10-4 s, linewidth, Δλ = 1 nm, and the speed of light, c = 3 x 108 m/s.
Thus, the stimulated emission cross-section σ = (λ2/2πc)2(τsp/Δλ) = 1.67 x 10-23 m2.
The pump efficiency, η = 1, and the saturation efficiency, ηst = 0.5. Therefore, the gain coefficient, G = 1.67 x 10-23(1/0.5)(1017-0) = 3.34 x 10-6 m-1.
(c) The total gain, Gtot = exp(2gL), where L is the length of the laser cavity. Solving for L, we get L = ln(Gtot)/2g.
Thus, the resonator should be L = ln(4)/2g to provide the total gain of 4.
Learn more about resonator here:
https://brainly.com/question/32273580
#SPJ11
Two hollow metal spheres are concentric with each other. The inner sphere has a radius of 0.130 m and a potential of 88.5 V. The radius of the outer sphere is 0.154 m and its potential is 74.3 V. If the region between the spheres is filled with Teflon, find the electric energy contained in this space. Number Units
Two hollow metal spheres are concentric with each other. The inner sphere has a radius of 0.130 m and a potential of 88.5 V. the electric energy contained in the space between the spheres is zero.
To find the electric energy contained in the space between the concentric spheres, we need to calculate the electric potential energy. The electric potential energy (U) can be calculated using the formula:
U = q * V,
where q is the charge and V is the electric potential.
Since the region between the spheres is filled with Teflon, which is an insulator, the charge on the inner sphere induces an equal and opposite charge on the outer sphere. Therefore, the total charge between the spheres is zero.
The electric potential difference (ΔV) between the spheres can be calculated by subtracting the potential of the inner sphere from the potential of the outer sphere:
ΔV = V_outer - V_inner
= 74.3 V - 88.5 V
= -14.2 V
Since the charge is zero, the electric potential energy (U) in the space between the spheres is also zero. This is because the electric potential energy depends on the product of charge and potential, and since the charge is zero, the energy is zero.
Therefore, the electric energy contained in the space between the spheres is zero.
Learn more about electric potential energy here:
https://brainly.com/question/28444459
#SPJ11
Distance Conversion, Light Years to Kilometers (Parallel B) Express the answer in scientific notation. A star is 9.6 light-years (ly) away from Earth. What is this distance in kilometers? d=×10 km
The distance from Earth to the star is approximately 9.07584 × 10^13 kilometers.
One light-year is the distance that light travels in one year. To convert light-years to kilometers, we need to multiply the given distance in light-years by the conversion factor, which is the distance traveled by light in one year. The speed of light is approximately 299,792 kilometers per second, and there are 31,536,000 seconds in a year (assuming a non-leap year).
So, the conversion factor is:
1 light-year = (299,792 km/s) * (31,536,000 s/year)
To find the distance in kilometers, we multiply the given distance of 9.6 light-years by the conversion factor:
d = 9.6 light-years * (299,792 km/s) * (31,536,000 s/year)
Calculating the above expression, we find that the distance is approximately 9.07584 × 10^13 kilometers.
Learn more about light-year here:
https://brainly.com/question/14534942
#SPJ11
(b) Estimate the pressure on the mountains underneath the Antarctic ice sheet, which is typically 3 km thick. (Density of ice = 917 kg/m³, g = 9.8 m/s²) Pressure 9170009
The estimated pressure on the mountains underneath the Antarctic ice sheet is approximately 26,854,200 N/m². To estimate the pressure on the mountains underneath the Antarctic ice sheet, we can use the formula for pressure:
Pressure = Density * g * Depth
Given:
Density of ice (ρ) = 917 kg/m³
Acceleration due to gravity (g) = 9.8 m/s²
Depth of the ice sheet (h) = 3 km = 3000 m
Plugging in these values into the formula, we get:
Pressure = 917 kg/m³ * 9.8 m/s² * 3000 m
= 26,854,200 N/m²
Therefore, the estimated pressure on the mountains underneath the Antarctic ice sheet is approximately 26,854,200 N/m².
To know more about Acceleration
brainly.com/question/31946450
#SPJ11
An RL circuit is composed of a 12 V battery, a 6.0 Hinductor and a 0.050 Ohm resistor. The switch is closed at t = 0 The time constant is 1.2 minutes and after the switch has been closed a long time the voltage across the inductor is zero. The time constant is 2.0 minutes and after the switch has been closed a long time the voltage across the inductor is 12 V. The time constant is 1.2 minutes and after the switch has been closed a long time the voltage across the inductor is 12 V. The time constant is 2.0 minutes and after the switch has been closed a long time the current is
An RL circuit is composed of a 12 V battery, a 6.0 Hinductor and a 0.050 Ohm resistor. Therefore, After the switch has been closed a long time the current is 240A.
The RL circuit composed of a 12 V battery, a 6.0 H inductor, and a 0.050 Ohm resistor, with the switch closed at t=0.
The time constant, denoted as τ, is a measure of the rate at which the voltage or current in a capacitor or inductor changes during the charging/discharging phase.
The time constant is determined by the product of the resistance (R) and capacitance (C) or inductance (L).
The voltage across an inductor is given by the formula V = L(di/dt), where L is the inductance in henries, and di/dt is the rate of change of current with respect to time.
When the voltage across the inductor is zero, this means that the current is constant, and therefore there is no rate of change of current with respect to time, di/dt = 0.
When the voltage across the inductor is equal to the source voltage (12V), this means that the inductor is fully charged, and therefore the current in the circuit is constant.
In this case, the inductor acts like a wire, and the voltage across the resistor is equal to the source voltage, Vr = 12V.
The time constant, τ, of the circuit is given by τ = L/R. Therefore, the time constant of the circuit is 1.2 minutes when the voltage across the inductor is zero and when the voltage across the inductor is 12V.
The time constant of the circuit is 2.0 minutes when the current in the circuit is constant and equal to I = V/R = 12/0.050 = 240 A.
Therefore, After the switch has been closed a long time the current is 240A.
Learn more about capacitance (C) here:
https://brainly.com/question/31871398
#SPJ11
A Carnot refrigeration cycle is used to maintain a room at
23 °C by removing heat from groundwater at 15 °C.
Refrigerant R-134a enters the condenser as saturated
vapor at 40 °C and leaves as saturated liquid at the
same temperature. The evaporator pressure is 351 kPa.
a) If the room is to receive 2kW, what is power input to
the compressor?
b) Net power input to cycle?
a) The power input to the compressor in the Carnot refrigeration cycle, in order to supply 2 kW of cooling to the room, will depend on the efficiency of the cycle and the heat transfer involved.
b) The net power input to the cycle can be determined by considering the work done by the compressor and the work done on the system.
a) To calculate the power input to the compressor, we need to determine the heat transfer from the groundwater to the room. The Carnot refrigeration cycle is an idealized cycle, and its efficiency is given by the equation: Efficiency = 1 - (T_evaporator / T_condenser), where T_evaporator and T_condenser are the temperatures at the evaporator and condenser, respectively. Using this efficiency, we can calculate the heat transfer from the groundwater and convert it to power input.
b) The net power input to the cycle takes into account the work done by the compressor and the work done on the system. It can be calculated by subtracting the work done by the compressor from the heat transfer from the groundwater. The work done by the compressor can be determined using the power input calculated in part a), and the heat transfer from the groundwater can be obtained using the given temperatures and the specific heat properties of the refrigerant.
Overall, the Carnot refrigeration cycle involves several calculations to determine the power input to the compressor and the net power input to the cycle, considering the heat transfer and work done in the system.
To know more about the Carnot refrigeration cycle click here:
https://brainly.com/question/29234662
#SPJ11
A 0.350 T magnetic field points due east, and is directed 30 above the horizontal (a) Find the force on a 4.0 micro-coulomb charge moving at 3 E6 m/s horizontally due south. Select) • Tim Atte 2 H Select (b) What is the direction of the force?
(a) the force on a 4.0 micro-coulomb charge moving at 3 E6 m/s horizontally due south is F = 1.68 ×[tex]10^{-8}[/tex] N
(b) the direction of the force is upward.
Given, Magnetic field, `B = 0.350 T` directed `30°` above the horizontal and the charge `q = 4.0 μC`, moving with velocity `v = 3 × [tex]10^6[/tex] m/s` horizontally due south.
(a) To find the force on the charge, we can use the formula,
F = q(v × B)
Here,`v × B` is the vector cross product of `v` and `B`.
Magnitude of the force,
F = qvB sin θ
Where, `θ` is the angle between `v` and `B`.
The direction of the force is perpendicular to both `v` and `B`.
Hence, the direction of the force is upward.
(b) `Upward` is the direction of the force on the charge.
To learn more about force, refer:-
https://brainly.com/question/30507236
#SPJ11
How many watts does a flashlight that has 6.4 x 10²C pass through it in 0.492 h use if its voltage is 3 V? __________ W
The power consumed by the flashlight is 10.92 W.
watt = volt x coulombs/sec
where:
watt = power
volt = voltage
coulombs/sec = charge/time
Put the given values in the formula, we get:
watt = 3 V × (6.4 × 10² C/0.492 h)
watt = 3 V × (6.4 × 10² C/1769.2 s)
watt = 10.92 W
Therefore, the power consumed by the flashlight is 10.92 W.
Learn more about power: https://brainly.com/question/11569624
#SPJ11
Water is poured into a U-shaped tube. The right side is much wider than the left side. Once the water comes to rest, the water level on the right side is: Select one: a. the same as the water level on the left side. b. higher than the water level on the left side. c. lower than the water level on the left side.
The correct answer is the same as the water level on the left side. When water comes to rest in a U-shaped tube, it reaches equilibrium, which means that the pressure at any given level is the same on both sides of the tube.
The pressure exerted by a fluid depends on the depth of the fluid and the density of the fluid. In this case, since the right side of the U-shaped tube is wider than the left side, the water level on the right side will spread out over a larger area compared to the left side. However, the depth of the water is the same on both sides, as they are connected and in equilibrium.
Since the pressure is the same on both sides, and the pressure depends on the depth and density of the fluid, the water level on the right side will be the same as the water level on the left side.
Therefore, option a. "the same as the water level on the left side" is the correct answer.
Learn more about pressure here:
https://brainly.com/question/857286
#SPJ11
A 1.25-kg wrench is acting on a nut trying to turn it. A force 135.0 N acts on the wrench at a position 12.0 cm from the center of the nut in a direction 35.0 ∘
above the horizontal handle. What is the 椽agnitude of the torque about the center of the nut? Be sure to give appropriate units.
The magnitude of the torque about the center of the nut is approximately 9.42 N.m, which is determined by multiplying the force acting on the wrench by the perpendicular distance between the force and the center of the nut.
To calculate the magnitude of the torque, we need to use the equation
τ = F * r * sin(θ),
where τ represents the torque, F is the force applied, r is the perpendicular distance between the force and the center of the nut, and θ is the angle between the force and the horizontal handle.
First, we convert the given distance from centimeters to meters: 12.0 cm = 0.12 m.
Next, we need to determine the perpendicular distance, r, by using trigonometry. Since the angle θ is given as [tex]35.0^0[/tex] above the horizontal handle, the angle between the force and the perpendicular line is ([tex]90^0 - 35.0^0) = 55.0^0[/tex]. Applying sine, we have [tex]sin(55.0^0) = r / 0.12 m[/tex].
Solving for r, we find r ≈ 0.097 m.
Finally, we can calculate the torque:
τ = (135.0 N) * (0.097 m) * sin([tex]35.0^0[/tex]).
Evaluating the expression, we find:
τ ≈ 9.42 N.m.
Therefore, the magnitude of the torque about the center of the nut is approximately 9.42 N·m.
Learn more about torque here:
https://brainly.com/question/30338175
#SPJ11
The resistance of a wire, made of a homogenous material with a uniform diameter, is proportional to its length. Select one: True False
False. The resistance of a wire made of a homogeneous material with a uniform diameter is not proportional to its length.
According to Ohm's law, the resistance (R) of a wire is determined by its resistivity (ρ), length (L), and cross-sectional area (A). The relationship is given by the equation R = ρ * (L/A). From this equation, we can see that the resistance depends on both the length and the cross-sectional area of the wire.
When the length of the wire increases, the resistance also increases. This is because the longer wire provides more obstacles for the flow of electric current, resulting in higher resistance. However, the relationship between resistance and length is not directly proportional but rather linear.
In a wire with a uniform diameter, the cross-sectional area remains constant throughout its length. Therefore, the resistance is directly proportional to the length of the wire, assuming the resistivity of the material remains constant.
Learn more about resistance here:
https://brainly.com/question/29427458
#SPJ11
The headlamp of a car take a current of 0.4A from a 12 volt the energy produced in 5 minutes is
Answer:
1440 J
Explanation:
Voltage (V) = 12 v
Current (I) = 0.4 A
Time (t) = 5min = 300sec
Power = Voltage x Current;
P = V x I = 12 x 0.4 = 4.8 W
We founded power, so for now we have to find energy. We will use another formula of power:
Power = Energy / Time
For now we will rearange the formula to find energy:
Energy = Power x Time;
E= P x t = 4.8W x 300sec = 1440 J
A disk 8.08 cm in radius rotates at a constant rate of 1 210 rev/min about its central axis. (a) Determine its angular speed. rad/s (b) Determine the tangential speed at a point 2.94 cm from its center. m/s (c) Determine the radial acceleration of a point on the rim. magnitude km/s2 direction ---Select--- (d) Determine the total distance a point on the rim moves in 2.02 s. m
Answer:
a) the angular speed is approximately 7608.47 rad/s.
b) the tangential speed is approximately 223.74 m/s.
c) the magnitude is approximately 468.16 km/s^2.
d) a point on the rim approximately 452.65 meters in 2.02 seconds.
(a) To determine the angular speed of the disk, we can convert the given rotational speed from rev/min to rad/s.
Radius (r) = 8.08 cm = 0.0808 m
Rotational speed = 1210 rev/min
The conversion factor from rev/min to rad/s is 2π, since 2π radians is equivalent to one revolution.
Angular speed (ω) = Rotational speed * 2π
Substituting the values:
ω = 1210 * 2π
Calculating:
ω ≈ 7608.47 rad/s
Therefore, the angular speed of the disk is approximately 7608.47 rad/s.
(b) To determine the tangential speed at a point 2.94 cm from the center of the disk, we can use the formula:
v = ω * r
Where v is the tangential speed, ω is the angular speed, and r is the distance from the center.
Distance from center (r) = 2.94 cm = 0.0294 m
Angular speed (ω) = 7608.47 rad/s
Substituting the values:
v = 7608.47 * 0.0294
Calculating:
v ≈ 223.74 m/s
Therefore, the tangential speed at a point 2.94 cm from the center of the disk is approximately 223.74 m/s.
(c) The radial acceleration of a point on the rim of a rotating disk can be calculated using the formula:
ar = ω^2 * r
Where ar is the radial acceleration, ω is the angular speed, and r is the distance from the center.
Distance from center (r) = 0.0808 m
Angular speed (ω) = 7608.47 rad/s
Substituting the values:
ar = (7608.47)^2 * 0.0808
Calculating:
ar ≈ 468.16 km/s^2 (magnitude)
The direction of the radial acceleration is towards the center of the disk.
Therefore, the magnitude of the radial acceleration of a point on the rim is approximately 468.16 km/s^2.
(d) To determine the total distance a point on the rim moves in 2.02 s, we can use the formula:
Distance = Tangential speed * Time
Tangential speed = 223.74 m/s
Time = 2.02 s
Substituting the values:
Distance = 223.74 * 2.02
Calculating:
Distance ≈ 452.65 m
Therefore, a point on the rim of the disk moves approximately 452.65 meters in 2.02 seconds.
Learn more about angular speed, here
brainly.com/question/6860269
#SPJ11
if the electric field is zero everywhere inside a region of space, the potential must also be zero in that region.
choices:
true always
true sometimes
false always
more info is needed
none of the above
The correct answer is "true always." If the electric field is zero everywhere inside a region of space, it implies that there are no electric field lines passing through that region.
This indicates that there are no potential differences between any points within the region.
In electrostatics, the potential is defined as the amount of work needed to move a unit positive charge from one point to another against the electric field.
If there is no electric field, no work is required to move the charge, meaning there is no potential difference. Therefore, the potential is zero throughout the region.
This relationship is a consequence of the fundamental property of conservative electric fields. In conservative fields, the electric field can be expressed as the gradient of a scalar function called the electric potential.
Consequently, if the electric field is zero, the gradient of the electric potential is also zero, implying a constant potential throughout the region.
Hence, when the electric field is zero everywhere inside a region of space, the potential must also be zero in that region.
To learn more about electric field lines visit:
brainly.com/question/21661975
#SPJ11
A cannon ball is launched into the ocean at an angle of 30° above the horizon. The cannonball has an initial speed of 46 m/s. The deck the cannonball is fired from is 11 meters high assume this is the initial height of the cannonball). a.) How long does the cannon ball take to reach the ocean? b.) What is the speed of the cannonball just before it lands in the ocean?
The speed of the cannon ball just before it lands in the ocean is given bythe resultant of the horizontal and vertical componentsv = √(vx² + vf²) = √(23 (√3)² + 32.32²)= √(1588.08) = 39.85 m/sHence, the speed of the cannon ball just before it lands in the ocean is 39.85 m/s.
a.) Time taken by the cannon ball to reach the ocean:The initial velocity of the cannon ball, u = 46 m/sThe angle made by the cannon ball with the horizontal, θ = 30°The vertical component of the initial velocity, v = u × sin θ = 46 × sin 30°= 46/2 = 23 m/sLet the time taken by the cannon ball to reach the ocean be t seconds.The distance covered by the cannon ball in the vertical direction in time t is given byh = ut + 1/2gt²where, g = acceleration due to gravity = 9.8 m/s²Substituting the values,11 = (23)t - 1/2 × 9.8 × t²11 = 23t - 4.9t²On solving this equation, we get two values of t, t = 0.947 seconds or t = 4.795 secondsThe time taken by the cannon ball to reach the ocean is 0.947 seconds.
b.) The speed of the cannonball just before it lands in the ocean:The horizontal component of the initial velocity of the cannon ball,vx = u × cos θ = 46 × cos 30°= 46(√3)/2 = 23 (√3) m/sThe time taken by the cannon ball to reach the ocean, t = 0.947 secondsThe horizontal distance covered by the cannon ball in time t is given byx = vx × t = 23 (√3) × 0.947 = 21.04 mThe vertical component of the final velocity of the cannon ball just before it lands in the ocean,vf = u + gt = 23 + 9.8 × 0.947 = 32.32 m/s
The speed of the cannon ball just before it lands in the ocean is given bythe resultant of the horizontal and vertical componentsv = √(vx² + vf²) = √(23 (√3)² + 32.32²)= √(1588.08) = 39.85 m/sHence, the speed of the cannon ball just before it lands in the ocean is 39.85 m/s.
Learn more about Speed here,
https://brainly.com/question/13943409
#SPJ11
A projectile is fired from the edge of a cliff at a height of 20.0 m as shown in the figure. The initial velocity vector is 200.0 m/s at an angle of 30 0
. The projectile reaches maximum height at point P and then falls and strikes the ground at point Q. How high is point P above point Q( in meters), assuming no air resistance? (rounded off to three SF). 128 m 490 m 940 m
The height of point P above point Q is approximately 530 m
In the figure shown below, a projectile is fired from the edge of a cliff at a height of 20.0 m.
The initial velocity vector is 200.0 m/s at an angle of 30 degrees. The projectile reaches maximum height at point P and then falls and strikes the ground at point Q. The vertical motion and horizontal motion of the projectile are independent of each other. We will first use the vertical component to figure out the time taken to reach the maximum height and the maximum height reached by the projectile.
The projectile's initial vertical velocity is v₀y = 200 sin(30°) = 100 m/s.
At the highest point, the projectile's vertical velocity is zero (v = 0) since it is momentarily at rest. The time taken for the projectile to reach the maximum height is given by:
v = v₀y + gtv = 0, v₀y = 100, g = -9.8 (taking downwards as the positive direction)t = v / g = v₀
y / g = 100 / 9.8 ≈ 10.204 s
The maximum height reached by the projectile is given by:
s = v₀yt + 1/2 gt² = 100 * 10.204 + 1/2 * (-9.8) * (10.204)²≈ 510.204 m
The horizontal velocity of the projectile is given by:
v₀x = 200 cos(30°) = 173.2 m/s.
The horizontal distance covered by the projectile from the edge of the cliff to the point of impact on the ground is given by:
x = v₀x * t = 173.2 * 10.204 ≈ 1770.51 m
The height of point P above point Q is the difference between the height of the cliff and the height of the point of impact on the ground. Hence, the height of point P above point Q is given by:
20.0 + 510.204 - 0 = 530.204 ≈ 530 m
Therefore, the height of point P above point Q is approximately 530 m (rounded off to three significant figures).
To learn about velocity here:
https://brainly.com/question/80295
#SPJ11
A cave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. The lift is performed in three stages, each requiring a vertical distance of 14.0 m: (a) the initially stationary spelunker is accelerated to a speed of 4.70 m/s; (b) he is then lifted at the constant speed of 4.70 m/s; (c) finally he is decelerated to zero speed. How much work is done on the 75.0 kg rescue by the force lifting him during each stage? (a) Number ___________ Units _____________
(b) Number ___________ Units _____________
(c) Number ___________ Units _____________
Work done in accelerating the rescue: 7841.25 Joules. Work done when lifting at a constant speed: 10296.3 Joules. Work done in decelerating the rescue: -7841.25 Joules.
(a) Mass of the rescue, m = 75.0 kg
Initial velocity, u = 0 m/s
Final velocity, v = 4.70 m/s
Vertical distance covered in each stage, d = 14.0 m (for stage a)
The work done in accelerating the rescue can be calculated using the work-energy principle:
Work = Change in kinetic energy
The change in kinetic energy is equal to the final kinetic energy deducted by the initial kinetic energy:
Change in kinetic energy = (1/2) * m * v^2 - (1/2) * m * u^2
Since the initial velocity is zero, the initial kinetic energy term becomes zero:
Change in kinetic energy = (1/2) * m * v^2
Change in kinetic energy = (1/2) * 75.0 kg * (4.70 m/s)^2
Calculating the work:
Work = Change in kinetic energy * Distance
Work = (1/2) * 75.0 kg * (4.70 m/s)^2 * 14.0 m
Calculating the result:
Work = 7841.25 Joules
So, the work done on the 75.0 kg rescue during stage (a) is 7841.25 Joules.
(b )Lifted at a constant speed of 4.70 m/s:
In this stage, the spelunker is lifted at a constant speed, which means there is no change in kinetic energy. The force required to lift the spelunker at a constant speed is equal to the gravitational force acting on them.
Mass of the rescue, m = 75.0 kg
Acceleration due to gravity is 9.81 m/s^2.
Vertical distance covered in each stage, d = 14.0 m (for stage b)
The work done in this stage can be calculated as:
Work = Force * Distance
The force required to lift the rescue at a constant speed is equal to their weight:
Force = Weight = m * g
Force = 75.0 kg * 9.81 m/s^2
Calculating the work:
Work = Force * Distance = (75.0 kg * 9.81 m/s^2) * 14.0 m
Calculating the result:
Work = 10296.3 Joules
Therefore, the work done on the 75.0 kg rescue during stage (b) is 10296.3 Joules.
(c) Decelerated to zero speed:
In this stage, the spelunker is decelerated to zero speed, which means their final velocity is zero.
Mass of the rescue, m = 75.0 kg
Initial velocity, u = 4.70 m/s
Final velocity, v = 0 m/s
Vertical distance covered in each stage, d = 14.0 m (for stage c)
The work done in decelerating the rescue can be calculated using the work-energy principle:
Work = Change in kinetic energy
The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy:
Change in kinetic energy = (1/2) * m * v^2 - (1/2) * m * u^2
Since the final velocity is zero, the final kinetic energy term becomes zero:
Change in kinetic energy = - (1/2) * m * u^2
Substituting the given values:
Change in kinetic energy = - (1/2) * 75.0 kg * (4.70 m/s)^2
Calculating the work:
Work = Change in kinetic energy * Distance
Work = - (1/2) * 75.0 kg * (4.70 m/s)^2 * 14.0 m
Calculating the result:
Work = - 7841.25 Joules
Therefore, the work done on the 75.0 kg rescue during stage (c) is -7841.25 Joules.
Learn more about Work done at: https://brainly.com/question/28356414
#SPJ11
A helicopter lifts a 82 kg astronaut 19 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/10. How much work is done on the astronaut by (a) the force from the helicopter and (b) the gravitational force on her? Just before she reaches the helicopter, what are her (c) kinetic energy and (d) speed? (a) Number ______________ Units _____________
(b) Number ______________ Units _____________
(c) Number ______________ Units _____________
(d) Number ______________ Units _____________
Answer: (a) The work done on the astronaut by the force from the helicopter is 1528.998 J. The units of work are Joules.
(b) The work done on the astronaut by the gravitational force on her is 15284.98 J. The units of work are Joules.
(c) The kinetic energy of the astronaut just before she reaches the helicopter is 15224.22 J. The units of work are Joules.
(d) Therefore, her speed just before she reaches the helicopter is 7.26 m/s. The units of speed are m/s.
Mass of the astronaut, m = 82 kg
Height to which the astronaut is lifted, h = 19 m
Acceleration of the astronaut, a = g/10 = 9.81/10 m/s² = 0.981 m/s²
(a) Work done
W = Fd
Here, d = h = 19 m,
The force applied, F = ma
F = 82 x 0.981
= 80.442 N.
Work done on the astronaut by the force from the helicopter, W₁ = FdW₁ = 80.442 x 19 = 1528.998 J.
The work done on the astronaut by the force from the helicopter is 1528.998 J. The units of work are Joules.
(b) The work done on the astronaut by the gravitational force on her is given by the product of the force of gravity and the displacement of the astronaut.
W = mgd
Here, d = h = 19 m
The gravitational force acting on the astronaut, mg = 82 x 9.81 = 804.42 N.
Work done on the astronaut by the gravitational force on her, W₂ = mgdW₂ = 804.42 x 19 = 15284.98 J.
The work done on the astronaut by the gravitational force on her is 15284.98 J. The units of work are Joules.
(c) Before the astronaut reaches the helicopter, her potential energy is converted into kinetic energy.
Therefore, the kinetic energy of the astronaut just before she reaches the helicopter is equal to the potential energy she has at the height of 19 m.
Kinetic energy of the astronaut, KE = Potential energy at 19 m.
KE = mgh
KE = 82 x 9.81 x 19
KE = 15224.22 J.
The kinetic energy of the astronaut just before she reaches the helicopter is 15224.22 J. The units of work are Joules.
(d) The kinetic energy of the astronaut just before she reaches the helicopter is equal to the work done on her by the force from the helicopter just before she reaches the helicopter. So,
KE = W₁
Therefore, her speed just before she reaches the helicopter can be found by equating the kinetic energy to the work done on her by the force from the helicopter and solving for velocity.
KE = 1/2 mv²
v = √(2KE/m)
v = √(2 x 1528.998/82)
v = 7.26 m/s.
Therefore, her speed just before she reaches the helicopter is 7.26 m/s. The units of speed are m/s.
Learn more about work done : https://brainly.com/question/25573309
#SPJ11
Dara and Cameron are studying projectile motion in their physics lab class. They set up a Pasco projectile launcher on the edge of their lab table, so that the ball will be launched at an initial height of H=33.5 inches, initial velocity of v
0
=3.4 m/s and an initial angle of θ 0
=37 ∘
(see diagram). They can then record the landing location by placing a piece of carbon paper on the floor some distance away from the launcher. When the ball lands, it will make a mark on the carbon paper. a) Find horizontal component of initial velocity (two significant figures please). σ 4
b) Find vertical component of initial velocity (two significant figures please). β c) Find the maximum height of the motion (two significant figures please). d) Find the landing location on carbon paper (three significant figures this time).
a) The horizontal component of initial velocity is 2.722 m/s.b) The vertical component of initial velocity is 2.023 m/s.c) The maximum height of the motion is 0.982 m.d) The landing location on carbon paper is 1.746 m.
Projectile motion is the path of an object through the air when it's acted upon by gravity. It's described as a two-dimensional motion since the object is moving in two directions. It has horizontal and vertical components, and each component is independent of the other. It can be calculated with the help of horizontal and vertical components of initial velocity, time, and acceleration due to gravity.
Projectile motion can be studied with the help of a Pasco projectile launcher, and it involves finding the horizontal component of initial velocity, vertical component of initial velocity, maximum height of the motion, and the landing location on carbon paper.a) To find the horizontal component of initial velocity, we can use the following formula:v₀ = v₀ cos(θ₀)Where v₀ is the initial velocity, and θ₀ is the initial angle. We're given:v₀ = 3.4 m/sθ₀ = 37°.
Therefore:v₀ = 3.4 cos(37°)v₀ ≈ 2.722 m/sThe horizontal component of initial velocity is 2.722 m/s. (to two significant figures)b) To find the vertical component of initial velocity, we can use the following formula:v₀ = v₀ sin(θ₀)Where v₀ is the initial velocity, and θ₀ is the initial angle. We're given:v₀ = 3.4 m/sθ₀ = 37°Therefore:v₀ = 3.4 sin(37°)v₀ ≈ 2.023 m/sThe vertical component of initial velocity is 2.023 m/s. (to two significant figures)c) To find the maximum height of the motion, we can use the following formula:y = H + v₀² sin²(θ₀) / 2gWhere H is the initial height, v₀ is the initial velocity, θ₀ is the initial angle, and g is the acceleration due to gravity.
We're given:H = 33.5 in = 0.8509 mv₀ = 3.4 m/sθ₀ = 37°g = 9.81 m/s²Therefore:y = 0.8509 + (3.4² sin²(37°)) / (2 x 9.81)y ≈ 0.982 mThe maximum height of the motion is 0.982 m. (to two significant figures)d) .
To find the landing location on carbon paper, we can use the following formula:x = v₀ cos(θ₀) tWhere v₀ is the initial velocity, θ₀ is the initial angle, and t is the time taken. The time taken can be calculated with the help of the following formula:y = H + v₀ sin(θ₀) t - 1/2 g t²Where H is the initial height, v₀ is the initial velocity, θ₀ is the initial angle, and g is the acceleration due to gravity. We're given:H = 33.5 in = 0.8509 mv₀ = 3.4 m/sθ₀ = 37°g = 9.81 m/s²We can convert the initial height into meters:0.8509 m = 2.79 ftv₀y = v₀ sin(θ₀) = 2.023 m/st = v₀y / g + sqrt(2gh) / gWe can plug in the values: t = 2.023 / 9.81 + sqrt(2 x 9.81 x 0.8509) / 9.81t ≈ 0.421 sThe time taken is 0.421 seconds. (to three significant figures).
Now we can find the landing location:x = v₀ cos(θ₀) tWhere v₀ is the initial velocity, θ₀ is the initial angle, and t is the time taken. We're given:v₀ = 3.4 m/sθ₀ = 37°t = 0.421 sTherefore:x = 3.4 cos(37°) x 0.421x ≈ 1.746 mThe landing location on carbon paper is 1.746 m. (to three significant figures)
Answer:a) The horizontal component of initial velocity is 2.722 m/s. (to two significant figures)b) The vertical component of initial velocity is 2.023 m/s. (to two significant figures)c) The maximum height of the motion is 0.982 m. (to two significant figures)d) The landing location on carbon paper is 1.746 m. (to three significant figures)
Learn more about Pasco projectile here,
https://brainly.com/question/8104921
#SPJ11
A long straight wire (diameter =3.2 mm ) carries a current of 19 A. What is the magnitude of the magnetic field 0.8 mm from the axis of the wire? (Note: the point where magnetic field is required is inside the wire). Write your answer in milli- tesla Question 7 A long solenoid (1,156 turns/m) carries a current of 26 mA and has an inside diameter of 4 cm. A long wire carries a current of 2.9 A along the axis of the solenoid. What is the magnitude of the magnetic field at a point that is inside the solenoid and 1 cm from the wire? Write your answer in micro-tesla.
The magnitude of the magnetic field at a point that is inside the solenoid and 1 cm from the wire is 24.6 micro-tesla.
The magnetic field can be calculated as follows: B = μ₀ I/2 r (for a current carrying long straight wire) where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the wire axis.
Magnetic field due to a current-carrying wire can be expressed using the equation:
B = μ₀ I / 2 r,
Where, μ₀ = 4π x 10⁻⁷ T m/AB = μ₀ I / 2 r = 4 x π x 10⁻⁷ x 19 / 2 x (0.8 x 10⁻³) = 7.536 x 10⁻⁴ T = 753.6 mT (rounded off to 1 decimal place)
The magnitude of the magnetic field at a point 0.8 mm from the axis of the wire is 753.6 milli-Tesla.
The magnitude of the magnetic field at a point inside the solenoid 1 cm from the wire can be calculated using the equation:
B = μ₀ NI / L, Where, μ₀ = 4π x 10⁻⁷ T m/AN is the number of turns per unit length of the solenoid
L is the length of the solenoid
B = μ₀ NI / L = 4π x 10⁻⁷ x 1156 x 26 x 10⁻³ / 0.04m = 24.57 x 10⁻⁶ T = 24.6 µT (rounded off to 1 decimal place)
Hence, the magnitude of the magnetic field at a point that is inside the solenoid and 1 cm from the wire is 24.6 micro-tesla.
To learn about magnetic fields here:
https://brainly.com/question/14411049
#SPJ11
The note Middle A on a piano has a frequency of 440 Hz. a. If someone is playing Middle A on the piano and you want to hear Middle B instead (493.883 Hz), with what velocity should you move? b. How about if you want Middle C (256 Hz)? c. What is the wavelength of Middle C?
a. To hear Middle B (493.883 Hz) instead of Middle A (440 Hz) on the piano, you should move with a velocity that is 12% faster than your current velocity.
b. To hear Middle C (256 Hz) instead of Middle A (440 Hz) on the piano, you should move with a velocity that is approximately 49% slower than your current velocity.
c. For Middle C (256 Hz), the wavelength would be approximately 1.34 meters.
The frequency of a sound wave is directly proportional to the velocity of the source. To hear a higher frequency (Middle B) than the original frequency (Middle A), you need to increase your velocity. Since Middle B has a frequency that is 12% higher than Middle A, you would need to increase your velocity by approximately 12%.
Conversely, to hear a lower frequency (Middle C) than the original frequency (Middle A), you need to decrease your velocity. Middle C has a frequency that is approximately 42% lower than Middle A, so you would need to slow down your velocity by approximately 49% to hear Middle C.
The wavelength of a sound wave can be calculated using the formula λ = v/f, where λ represents the wavelength, v represents the velocity of sound, and f represents the frequency. For Middle C with a frequency of 256 Hz and assuming a velocity of sound in air of approximately 343 meters per second, the wavelength is calculated to be approximately 1.34 meters. This means that the distance between two consecutive peaks or troughs of the sound wave is 1.34 meters.
Learn more about wavelength here:
https://brainly.com/question/31322456
#SPJ11
In the following circuit, the two diodes are identical with a transfer characteristic shown in the figure. For an input with triangular waveform and circuit components listed in the table, answer the following questions. Table 1 Circuit Parameters a) find Vin ranges that turns diodes ON or OFF? b) draw circuit transfer characteristic (Vout versus Vin)? Vcc 4 [V] VON 1 [V] R₁ R₁ D₂ 2k [Ω] R₂ 1k [92] ww Vout R₂ 1k [92] ਨੀਤੀ D₁ R₂ Vin (N) KH Table 2. Answers Vout +Vcc T-Vcc R3 Vin VON V₂ Both Diodes OFF One Diode ON and the Other Diode OFF Both Diodes ON Vin Vin>-2V -3V
In the given circuit,
a) if the input voltage is between -1V to 1V, then one diode will be ON and the other diode will be OFF. If the input voltage is greater than 1V, then both diodes will be ON.
b) the transfer characteristic for the circuit is:
Vout = (1/3) * Vin
a) Vin ranges that turn diodes ON or OFF
In the given circuit, the two diodes are identical with a transfer characteristic shown in the figure.
For an input with triangular waveform and circuit components listed in the table, the Vin ranges that turn diodes ON or OFF are:
If the input voltage is less than -1V, then both the diodes will be OFF. If the input voltage is between -1V to 1V, then one diode will be ON and the other diode will be OFF. If the input voltage is greater than 1V, then both diodes will be ON.
b) Circuit transfer characteristic (Vout versus Vin)The transfer characteristic (Vout versus Vin) for the given circuit is shown below:
the transfer characteristic for the circuit is:
Vout = (1/3) * Vin
Thus if the input voltage is less than -1V, then both the diodes will be OFF. If the input voltage is between -1V to 1V, then one diode will be ON and the other diode will be OFF. If the input voltage is greater than 1V, then both diodes will be ON and the transfer characteristic for the circuit is Vout = (1/3) * Vin
Learn more about diode https://brainly.com/question/16767330
#SPJ11
Ocean waves with a wavelength of 10 m and a frequency of 0.2 Hz strike an opening (width = 10 m) in a seawall straight on. If a flat beach is parallel to the seawall and 200 m from it, (a) where on the beach will the water flow the farthest inland and (b) where does the water at the beach barely move at all?
(a) The maximum displacement of the waves from the mean position on the shore is given by
d(max) = 2*a,
where "a" is the amplitude of the wave.
The amplitude is given by the product of the wave's speed (v), frequency (f) and wavelength (λ).
v = λ*f = (10 m)(0.2 Hz) = 2 m/s.a = (1/2)v/f = (1/2)(2 m/s)/(0.2 Hz) = 5 m.d(max) = 2*a = 10 m
Therefore, the maximum displacement of the waves from the mean position on the shore is 10 m. The farthest point of the beach that the waves will reach is therefore 200 m + 10 m = 210 m from the seawall.
(b) The point of the beach at which the waves barely move at all is called the node. At the node, the displacement of the waves from the mean position is zero.
The location of the node is given by the formula:
x = n*(λ/2),where n is an integer. Since the width of the opening in the seawall is 10 m, the waves that will strike the seawall must have a wavelength of 10 m.
Therefore,λ = 10 m.x = n*(λ/2) = n*(10/2) = 5n m
To find the nodes, we need to find the values of n that make x a multiple of 5 m. Therefore, the nodes are located at every 5 m along the shore starting from 200 m, i.e., 200 m, 205 m, 210 m, 215 m, ...The water at the beach will barely move at all at the nodes.
Therefore, the locations of the nodes are where the water on the beach barely moves.
Learn more about maximum displacement here
https://brainly.com/question/30266030
#SPJ11
Two motorcycles start at the intersection of two roads which make an angle of 600 which each other. Motorcycle A accelerate at 0.90 m/s2. Motorcycle B has an acceleration of 0.75 m/s2. Determine the relative displacement in meters. 20 seconds after leaving the intersection. Group of answer choices 167.03 143.89 172.12 156.23 122.45
The relative displacement between Motorcycle A and Motorcycle B, 20 seconds after leaving the intersection, is 210 meters.
To determine the relative displacement between Motorcycle A and Motorcycle B, we need to find the individual displacements of each motorcycle after 20 seconds and then find the difference between them.
Let's calculate the displacements:
For Motorcycle A:
Using the kinematic equation: displacement = initial velocity * time + (1/2) * acceleration * time^2
The initial velocity of Motorcycle A is 0 m/s since it starts from rest.
The acceleration of Motorcycle A is 0.90 m/s^2.
The time is 20 seconds.
So, the displacement of Motorcycle A after 20 seconds is:
displacement_A = 0 * 20 + (1/2) * 0.90 * (20)^2
displacement_A = 0 + 0.9 * 400
displacement_A = 360 meters
For Motorcycle B:
Using the same kinematic equation:
The initial velocity of Motorcycle B is 0 m/s.
The acceleration of Motorcycle B is 0.75 m/s^2.
The time is 20 seconds.
So, the displacement of Motorcycle B after 20 seconds is:
displacement_B = 0 * 20 + (1/2) * 0.75 * (20)^2
displacement_B = 0 + 0.375 * 400
displacement_B = 150 meters
Now, let's find the relative displacement by subtracting the displacement of Motorcycle B from the displacement of Motorcycle A:
relative displacement = displacement_A - displacement_B
relative displacement = 360 - 150
relative displacement = 210 meters
To know more about kinematic equation
https://brainly.com/question/24458315
#SPJ11
Electric Field a the Mid-Point of Two Charges The electric Field midway between two equal but opposite point charges is 1920 N/C, and the distance between the charges is 11.4 cm. What is the magnitude of the charge on each?
Given:
Electric field midway between two equal but opposite point charges is 1920 N/C. Distance between the charges is 11.4 cm.
Let q be the magnitude of the charge on each point charge.
Using Coulomb's law, the electric field E due to a point charge q at a distance r from it is given by;
E = kq/r
where k = 9 × 10^9 Nm²/C² is Coulomb's constant.
It follows that the electric field E at the midpoint between the two charges is given by;
E = (1/4πε₀) [2q/(11.4/2)²] = 1920 N/C
Where ε₀ is the permittivity of free space.
Evaluating for q;
q = E(11.4/2)²(4πε₀)/2
= 7.7 × 10^-6C (rounded off to 2 significant figures)
Therefore, the magnitude of the charge on each point charge is 7.7 × 10^-6 C.
What is an electric field?
An electric field is defined as a field of force surrounding an electrically charged particle that exerts a force on another charged particle that comes within its field of influence.
Learn more about permittivity of free space here
https://brainly.com/question/30403318
#SPJ11
A 1.15 kg copper bar rests on two horizontal rails 0.95 cm apart and carries a current of 53.2 A from one rail to the other. The coefficient of static friction is 0.58. Find the minimum magnetic field (not necessarily vertical) that would cause the bar to slide. Draw a free body diagram to describe the system.
To determine the minimum magnetic field required to cause a copper bar, with a mass 1.15 kg or a current of 53.2 A, to slide on two horizontal rails spaced 0.95 cm apart, we can analyze forces acting on the bar.
A magnetic field is a physical field produced by moving electric charges, magnetic dipoles, or current-carrying conductors. It extends around a magnet or a current-carrying wire and exerts a force on other magnetic materials or moving charges. Magnetic field are responsible for the behavior of magnets and are crucial in various applications such as electric motors, generators, and magnetic resonance imaging (MRI) machines. They are described mathematically by the principles of electromagnetism and are often visualized using magnetic field lines.
Learn more about magnetic field here;
https://brainly.com/question/14411049
#SPJ11
You drop something from rest at a height of 1 meter, and it hits the ground after 1
second. What do you know about the object’s vertical motion? Circle all known quantities. Do not assume you are on Earth. Solve for the missing quantity or quantities using the appropriate big four kinematic formulas.
xi, Initial position
xf, Final position
vi, Initial velocity
vf, Final velocity
a, Acceleration
∆t, Change in time
The missing quantity is the acceleration (a) of the object's vertical motion. The negative sign indicates that the object is undergoing downward acceleration, which is expected for an object in free fall under the influence of gravity.
From the given information, we can identify the following known quantities:
xi = 1 meter (initial position)
xf = 0 meter (final position)
vi = 0 m/s (initial velocity)
∆t = 1 second (change in time)
Using the kinematic equation:
xf = xi + vit + (1/2)at^2
Substituting the known values:
0 = 1 + 0 + (1/2)a(1)^2
Simplifying the equation:
0 = 1 + (1/2)a
Solving for 'a':
a = -2 m/s^2
Note: The final velocity (vf) is not necessary to solve this problem since we are only interested in the object's motion while falling, not at the moment it hits the ground.
Learn more about initial velocityhere:
https://brainly.com/question/28395671
#SPJ11