State the difference between positive and negative zero error of a vernier calliper​

(a) To solve for the mass of the rod, we can use the formula for rotational kinetic energy:

KE = (1/2) * I * w^2

where KE is the rotational kinetic energy, I is the moment of inertia, and w is the angular velocity.

At the beginning, when the bug is at the axis of rotation, the rotational kinetic energy of the rod is:

KE1 = (1/2) * I * w^2 = (1/2) * (3.10×10−3 kg⋅m^2) * (0.37 rad/s)^2 = 0.036 J

When the bug reaches the other end of the rod, the rotational kinetic energy is:

KE2 = (1/2) * I * w^2 = (1/2) * (3.10×10−3 kg⋅m^2) * (0.132 m/s)^2 / (0.480 m)^2 = 3.62×10^-5 J

The change in kinetic energy is due to the work done by the bug as it crawls along the rod. The work done by the bug can be calculated as the product of the force it exerts on the rod and the distance it crawls:

W = F * d

The force the bug exerts on the rod can be calculated using Newton's second law for rotational motion:

τ = I * α

where τ is the torque, α is the angular acceleration, and I is the moment of inertia.

Since the rod is rotating with a constant angular velocity, its angular acceleration is zero, so the net torque on the rod must be zero. This means that the torque exerted by the bug on the rod must be equal and opposite to the torque due to the angular momentum of the rod:

τ_bug = τ_rod

F * d = I * w

F = I * w / d

Substituting the values given, we get:

F = (3.10×10−3 kg⋅m^2) * (0.37 rad/s) / (0.480 m) = 0.0237 N

Now we can use the work-energy principle to find the mass of the rod:

W = KE2 - KE1 = F * d = (1/2) * m * v^2

where m is the mass of the rod and v is the tangential velocity of the bug at the end of the rod.

Substituting the values given, we get:

(1/2) * m * (0.132 m/s)^2 = 3.62×10^-5 J - 0.036 J

Simplifying and solving for m, we get:

m = 0.221 kg

Therefore, the mass of the rod is 0.221 kg.

(b) To find the mass of the bug, we can use the same equation we used to calculate the force it exerted on the rod:

F = I * α / d

where α is the angular acceleration of the rod caused by the bug crawling along it.

Since the rod is a thin uniform rod, its moment of inertia can be calculated as:

I = (1/3) * m * L^2

where L is the length of the rod.

Substituting the values given, we get:

I = (1/3) * (0.221 kg) * (0.480 m)^2 = 0.0202 kg⋅m^2

Now we can calculate the angular acceleration caused by the bug crawling along the rod. Since the rod is rotating with a constant angular velocity, its angular acceleration is given by:

α

Fade

finish

α = (w_f^2 - w_i^2) / (2 * θ)

where w_i is the initial angular velocity of the rod, w_f is the final angular velocity of the rod after the bug has crawled to the end, and θ is the angle through which the bug crawls, which is equal to the length of the rod:

θ = L = 0.480 m

Substituting the values given, we get:

α = (0.132 m/s)^2 / (2 * 0.480 m) = 0.072 rad/s^2

Now we can calculate the force exerted by the bug on the rod:

F = I * α / d = (0.0202 kg⋅m^2) * (0.072 rad/s^2) / (0.480 m) = 0.00303 N

Finally, we can use Newton's second law to find the mass of the bug:

F = m * a

where a is the tangential acceleration of the bug, given by:

a = r * α

where r is the distance from the bug to the axis of rotation, which is equal to the length of the rod minus the distance the bug has crawled, or:

r = L - d = 0.480 m - 0.480 m = 0 m

Therefore, the tangential acceleration of the bug is zero, and its mass is:

m = F / a = 0.00303 N / 0 m/s^2 = undefined

This means that the force exerted by the bug on the rod is not enough to cause any tangential acceleration, and therefore the mass of the bug is negligible compared to the mass of the rod. We can assume that the bug has zero mass for practical purposes.

We can use the laws of physics to solve this problem. The key here is to recognize that the initial kinetic energy of the car (due to its speed) is converted into potential energy as it goes up the ramp, and then back into kinetic energy as it falls back down.

Using conservation of energy, we can set the initial kinetic energy equal to the final potential energy at the maximum height:

(1/2) * m * v^2 = m * g * h

where m is the mass of the car, v is its initial speed (30 m/s), g is the acceleration due to gravity (9.81 m/s^2), and h is the maximum height.

Simplifying the equation and solving for h, we get:

h = (v^2 * sin^2(theta)) / (2 * g)

where theta is the angle of the ramp (37 degrees in this case).

Plugging in the known values, we get:

h = (30^2 * sin^2(37)) / (2 * 9.81) ≈ 79.1 meters

So the car will reach a height of approximately 79.1 meters off the ground.

To find the maximum height of the gorge that the car could clear, we need to look at the horizontal distance that the car travels while in the air. This distance is given by:

d = v * t

where t is the time that the car spends in the air. We can find t by setting the initial potential energy (at the maximum height) equal to the final kinetic energy (at the end of the jump):

m * g * h = (1/2) * m * (v_f^2)

where v_f is the final velocity of the car at the end of the jump (when it lands back on the ground). We can solve for v_f using:

v_f = sqrt(2gh)

where h is the maximum height (found earlier). Plugging this into the conservation of energy equation, we get:

t = sqrt(2h/g)

Now we can plug in the known values for v and theta to get:

d = 30 * sqrt(2h/g) * cos(theta)

Plugging in the values for h and theta, we get:

d = 30 * sqrt(2*79.1/9.81) * cos(37) ≈ 187.2 meters

So the maximum height of the gorge that the car could clear is approximately 187.2 meters.

The force is 400.2 N

The work done is 120 J

The power is 48W

Force is a physical concept that describes the influence that one object has on another object, causing it to accelerate or deform. Force can be defined as any influence that changes the motion of an object, such as a push or a pull.

How to solve:

under equilibrium condition

F * 1.45 m =68 kg * 9.81 m/s^2 *0.87 m

F =400.2 N

b)

work done = m*g*h =68 kg*9.81 m/s^2*0.180 m =120.0744 J =120 J

c)

power =120.0744 J *(24 /60 s) =48.02976 W = 48 W

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Answer: the lowest note that would be possible to blow on this brass pipe is approximately 1700 Hz

Explanation: f = c / (2L)

where c is the speed of sound in brass, which is around 340 m/s.

Changing over the length of the pipe to meters, we have:

L = 10 cm = 0.1 m

Stopping within the values, we get:

f = 340 / (2 x 0.1) = 1700 Hz

Ammeter is always connected in series with the circuit in which the current is to be measured.

An ammeter is connected, to gauge the current flowing through a part or circuit. Since current in a series connection stays constant and an ammeter's resistance is relatively low, the current being measured is unaffected. For the purpose of measuring current, an ammeter is linked in series.

A shunt running parallel to the metre carries the majority of the current at high current values, hence an ammeter can measure a wide range of current values. An ammeter is represented by a circle with a capital A inside it on circuit diagrams.

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Okay, let's solve this step-by-step:

1) Given:

A → = 2.0 x ^ − 3.2 y ^

B → = − 1.2 x ^ + 2.9 y ^

Find: Angle between D → = A → − B → and positive x-axis

2) Subtract the vectors to find D →:

D → = 2.0 x ^ − 3.2 y ^ - (− 1.2 x ^ + 2.9 y ^ )

= 2.0 x ^ − 3.2 y ^ + 1.2 x ^ - 2.9 y ^

= 3.2 x ^ − 6.1 y ^

3) To find the angle, we use the inverse tangent ratio of y/x:

Angle = tan−1(−6.1/3.2) = -61.97°

4) Since the angle is in the 4th quadrant, it is measured clockwise from the positive x-axis. So the final angle is 180 - 61.97 = 118.03°

Therefore, the angle between the vector D → = A → − B → and the positive x-axis is 118.03°.

Let me know if you have any other questions!

The current in the circuit when AP is 40.0 cm is 2.5 A.

We can use Ohm's law to calculate the current in the circuit:

V = IR

where V is the voltage, I is the current, and R is the resistance.

The resistance of the wire AX can be calculated as:

R = ρ ([tex]\frac{L}{A}[/tex])

where ρ is the resistivity of the wire material, L is the length of the wire, and A is the cross-sectional area of the wire.

Since the resistance per unit length of wire AX is given as 2 [tex]\frac{ohm}{m}[/tex] ,we can calculate the resistance of a 40 cm length of wire AX as:

R = (2 [tex]\frac{ohm}{m}[/tex]) × ([tex]\frac{40 cm}{100 \frac{cm}{m}}[/tex]) = 0.8 ohm

Using the voltmeter reading across R as 2.0V and the battery voltage as 4.0V, we can calculate the voltage across the wire AX as:

V = 4.0V - 2.0V = 2.0V

Therefore, we can calculate the current in the circuit as:

I = [tex]\frac{V}{R}[/tex] = [tex]\frac{2.0V }{0.8 ohm}[/tex] = 2.5 A

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The magnitude of the force is 3.6 x 10^-6 N, rounded to two significant figures.

The magnitude of the force between two point charges can be calculated using Coulomb's law:

F = k * (q1 * q2) /[tex]r^2[/tex]

where F is the magnitude of the force in Newtons (N), k is Coulomb's constant (9 x 10^9 N*m^2/C^2), q1 and q2 are the magnitudes of the charges in Coulombs (C), and r is the distance between the charges in meters (m).

Plugging in the given values, we get:

F =[tex](9 * 10^{9} N*m^{2}/C^2) * (-0.0004\ C) * (0.0003 C) / (3 m)^{2}[/tex]

Simplifying the expression, we get:

F = [tex]-3.6 * 10^{-6} N[/tex]

Note that the negative sign in the result indicates that the force is attractive. The magnitude of the force is [tex]3.6 * 10^{-6} N[/tex], rounded to two significant figures.

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(a) The work input on the machine is 10 J.

(b) The work output of the machine is 80 J.

(b) The Machanical advantage of the machine is 20.

Machine is any device that enables work to be done easily.

(a) To calculate the work input of the machine, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

(b) Also, for work output, we use the formula below

Where:

Substitute these values into equation 2

(c) To calculate the mechanical advantage of the machine, we use the formula below

Given:

Substitute into equation 3

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Answer:

19.2 centimeters or 0.192 meters. Both are the same.

Explanation:

T = 2π√(L/g)

T = 60.0 s / 14 ≈ 4.29 s

L = (gT²) / (4π²) ≈ 0.384 m

h + 0.384 m = height above the field

H = h + 0.192 m

H = h

h ≈ 0.192 m or 19.2 cm.

Answer:

A. iron.

In the process of nuclear fusion, lighter elements are fused together to form heavier elements. This process releases energy and is what powers the star. However, the fusion of elements heavier than iron requires energy, rather than releasing it. Therefore, once a star has produced iron in its core, it is no longer able to sustain nuclear fusion and will eventually undergo a supernova explosion.

The magnifying glass should be held 16.4 cm away from the nickel to obtain an image with a magnification of +1.53.

Using the thin lens equation, 1/f = 1/o + 1/i, where f is the focal length, o is the object distance, and i is the image distance, and the magnification equation, M = -i/o, where M is the magnification, we can solve for the object distance.

First, solve for the image distance i:

M = -i/o

1.53 = -i/o

i = -1.53o

Then, substitute i into the thin lens equation:

1/0.103 = 1/o + 1/(-1.53o)

Solving for o, we get:

o = 16.4 cm

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D. The universe is expanding. Hubble's observation of red shift in the light from distant galaxies led him to conclude that these galaxies were moving away from us and that the universe was expanding.

Hubble's most famous observation was his discovery of the relationship between the redshift of light from distant galaxies and their distance from Earth. He observed that the light from distant galaxies was shifted toward longer, redder wavelengths, which indicated that the galaxies were moving away from us. By analyzing the degree of redshift, Hubble was able to calculate the distance of these galaxies from Earth and found that they were much farther away than previously thought. This led him to conclude that the universe was expanding and laid the foundation for the Big Bang theory.

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Okay, let's break this down step-by-step:

1) A neutron has a mass of 1.7 x 10-27 kg and an approximate radius of 1.2 x 10-15 m.

So we know the mass and radius of a single neutron.

2) The mass of the sun is 2.0 x 1030 kg.

So we know the total mass of the sun, which is much greater than a neutron.

3) When a massive star reaches the end of its life, it can explode as a supernova.

This supernova can form a neutron star.

4) A neutron star has a density about the same as a neutron.

So we can conclude that a neutron star has a density of:

Density = Mass / Volume

= (1.7 x 10-27 kg) / (4/3 * pi * (1.2 x 10-15 m)3)

= 1.6 x 1017 kg/m3

5) A neutron star forms from the core collapse of a massive star during supernova.

So it has a mass on the order of 1-2 times that of the sun (2 x 1030 kg),

but compressed into a sphere only about 10-20 km in radius.

So its mass would be huge, around 2 x 1030 kg, but confined to a tiny volume,

giving it an immense density, around 1.6 x 1017 kg/m3, the same as a neutron.

Does this help explain the concepts and walk through the calculations? Let me know if you have any other questions!

1.01 x 10-6 m/sec is the speed of advance of the glacier in m/s

1 foot = .3048 meters

105 ft = 105(.3048) = 32.004 m

(365.25 days)(24 hrs/day)(60 min/hr)(60 sec/min)

= 31,557,600 sec/yr

m/sec = 32.004/31557600 = 1.0141455624 x 10-6 m/sec

Round to 1.01 x 10-6 m/sec

Hubbard Glacier in Alaska has been slowly thickening and moving towards Disenchantment Bay since observations began in 1895. The progress contrasts with several neighbouring thinning and receding glaciers in Alaska and elsewhere in the world.

Hubbard Glacier's base ice is around 400 years old since it takes that long for ice to travel the glacier's entire length. Frequently, icebergs the size of a ten-story structure are calved off by the glacier.

Sea levels are rising as a result of glaciers, such those that cover Greenland, melting as a result of climate change.  

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The rich merchant can save himself by throwing some gold coins in one direction.

You finally remembered Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.

Newton's third rule of motion states that for every action, there is an equal and opposite reaction. When he tosses the gold coins in one direction, the flung coins cause a rebound force in the opposing direction. This recoil force will provide him with a little amount of velocity, which he may then employ to go in the opposite direction he tossed the coins. He can slowly make his way to the coast by continuing this method.

It is because the heavier hammer has more mass than the toy hammer, when the same force is applied to both hammers, the heavier hammer suffers less acceleration than the lighter hammer. This implies that the heavier hammer applies more power to the nail, making it easier to drive into the hard wood.

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(a) The impedance of the circuit at 485 Hz is approximately 1253.53 Ω.

(b) The impedance of the circuit at 7.50 kHz is approximately 1256.04 Ω.

(c) The current (Irms) at 485 Hz is approximately 326 mA, and the current at 7.50 kHz is approximately 325 mA.

(d)  The resonant frequency of the circuit is approximately 25.74 kHz.

(e) The current (Irms) at resonance is approximately 408 mA.

a) The impedance (Z) of an RLC series circuit can be calculated using the formula:

Z = √(R^2 + (ωL - 1/ωC)^2)

where;

Given:

R = 1.00 kΩ = 1000 Ω

L = 155 mH = 0.155 H

C = 25.0 nF = 25.0 × 10^(-9) F

f = 485 Hz

First, we need to convert the frequency from Hz to radians per second:

ω = 2πf

Substituting the given values into the impedance formula:

Z = √((1000)^2 + ((2π × 485) × 0.155 - 1/(2π × 485 × 25.0 × 10^(-9)))^2)

Calculating Z:

Z = √((1000)^2 + (481.663)^2) ≈ 1253.53 Ω

(b) Given:

f = 7.50 kHz = 7500 Hz

ω = 2πf

Substituting the given values into the impedance formula:

Z = √((1000)^2 + ((2π × 7500) × 0.155 - 1/(2π × 7500 × 25.0 × 10^(-9)))^2)

Calculating Z:

Z = √((1000)^2 + (568.28)^2) ≈ 1256.04 Ω

So, the impedance of the circuit at 7.50 kHz is approximately 1256.04 Ω.

(c) Given:

Vrms = 408 V

At 485 Hz:

Irms = Vrms / Z (using the impedance calculated in part (a))

Irms = 408 / 1253.53 ≈ 0.326 A = 326 mA

At 7.50 kHz:

Irms = Vrms / Z (using the impedance calculated in part (b))

Irms = 408 / 1256.04 ≈ 0.325 A = 325 mA

(d) The resonant frequency of an RLC circuit can be calculated using the formula:

f_resonant = 1 / (2π√(LC))

Given:

L = 155 mH = 0.155 H

C = 25.0 nF = 25.0 × 10^(-9) F

Substituting the given values into the resonant frequency formula:

f_resonant = 1 / (2π√(0.155 × 25.0 × 10^(-9)))

Calculating f_resonant:

f_resonant ≈ 25.74 kHz

(e) At resonance, the impedance of the inductor (ωL) and the capacitor (1/(ωC)) cancel each other out, resulting in the minimum impedance of the circuit.

Therefore, at resonance, the impedance (Z) of the circuit is equal to the resistance (R) only.

Given:

R = 1.00 kΩ = 1000 Ω

Vrms = 408 V

Using Ohm's law, we can calculate the current (Irms) at resonance:

Irms = Vrms / R

Irms = 408 / 1000 = 0.408 A = 408 mA

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Answer:m 1= 36 g=0.036 kg - the mass of ice T1= −77 ◦C. - temperature of ice m2=589 g=0.589 kg - mass of water C1=2090 J/kg · ◦C - specific heat of ice  λ = 3.33 × 10^5 J/kg - latent heat of fusion of water T2=26◦C. - temperature of water C2= 4186 J/kg · ◦C . - - specific heat of water m3=74 g=0.074kg - mass of copper T3=26◦C. - temperature of copper C3=387 J/kg ·◦C - specific heat of copper is and of ice is T - ? - final temperature  1  1 ( 0 −  1 ) −  ℎ  0  1  −  1  2 (  − 0 ) −  ℎ   2  2 (  −  2 ) −   3  3 (  −  3 ) −  m 1 ​ C 1 ​ (0−T 1 ​ )−ice heating to 0 o C m1λ−ice melting m 1 ​ C 2 ​ (T−0)−melted water heating m 2 ​ C 2 ​ (T−T 2 ​ )−water cooling m 3 ​ C 3 ​ (T−T 3 ​ )−copper cooling  1  1 ( 0 −  1 ) +  1  +  1  2 (  − 0 ) +  2  2 (  −  2 ) +  3  3 (  −  3 ) = 0 m 1 ​ C 1 ​ (0−T 1 ​ )+m1λ+m 1 ​ C 2 ​ (T−0)+m 2 ​ C 2 ​ (T−T 2 ​ )+m 3 ​ C 3 ​ (T−T 3 ​ )=0 0.036 ⋅ 2090 ⋅ 77 + 0.036 ⋅ 3.33 ⋅ 1 0 5 + 0.036 ⋅ 4186 ⋅  + 0.589 ⋅ 2090 ⋅ (  − 26 ) + 0.074 ⋅ 387 ⋅ (  − 26 ) = 0 0.036⋅2090⋅77+0.036⋅3.33⋅10 5 +0.036⋅4186⋅T+0.589⋅2090⋅(T−26)+0.074⋅387⋅(T−26)=0 1410.344 ⋅ = 14969.368  = 10.6 1  1410.344⋅T=14969.368 T=10.61 o C Answer:  = 10.6 1  T=10.61 o C

Explanation:

Answer:

The formula to calculate average speed is:

average speed = total distance / total time

In this case, the distance covered is 500 meters and the time taken is 14.5 minutes. However, we need to convert the time to seconds to get the answer in meters per second.

14.5 minutes = 14.5 x 60 seconds = 870 seconds

So, the average speed is:

average speed = total distance / total time

average speed = 500 meters / 870 seconds

average speed = 0.57 meters per second

Therefore, the average speed of the runner is 0.57 meters per second.