Q: A mass $$m = 0.05\ \mathrm{kg}$$ falls a height $$h = 0.4\ \mathrm{m}$$, pulling a cart of mass $$M = 0.2\ \mathrm{kg} on a $$frictionless air track. What is the final velocity $$v of $$the system? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{\frac{2mgh}{m+M}} = \sqrt{\frac{2 \times 0.05 \times 9.8 \times 0.4}{0.05+0.2}} \approx 1.25\ \mathrm{m/s}$$

Question 1

Which of the following statements best describes the difference between elastic and inelastic collisions as studied on the linear air track?

Accepted Answer

In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, only momentum is conserved.

Question 2

A cart of mass $$m_1 = 0.5$$\ \mathrm{kg}$$ moving at v_1$ = 2.0\ \mathrm{m/s}$$ collides elastically with a stationary cart of mass $$m_2 = 0.5$$\ \mathrm{kg}$$. What is the velocity of m_1$ after the collision?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 3

Which equation correctly expresses the conservation of momentum for a two-body collision in one dimension?

Accepted Answer

$$m_1$$ $$v_1$$ + $$m_2$$ $$v_2$$ = $$m_1$$ $$v_1$$' + $$m_2$$ $$v_2$$'$$

Question 4

During the gravitational potential energy experiment, a mass $$m$$ falls a height $$h$$ and pulls a cart of mass $$M on $$the air track. Which equation gives the final velocity $$v of $$the system, assuming no friction?

Accepted Answer

$$\frac{1}{2}(m+M)v^2$ = mgh$$

Question 5

If the air track is not properly leveled, what is the most likely effect on your velocity measurements?

Accepted Answer

The vehicles will accelerate due to gravity, making accurate velocity measurements impossible.

Question 6

A 0.2 kg cart moving at 1.5 m/s collides inelastically with a stationary 0.3 kg cart. What is their common velocity after the collision?

Accepted Answer

$$0.6\ \mathrm{m/s}$$

Question 7

Which of the following best explains why the linear air track is used in collision experiments?

Accepted Answer

It minimizes friction, allowing for more accurate measurements of momentum and energy.

Question 8

In the experiment, why is it important to determine the effective length of the vehicle's card when using the digitimer and light gates?

Accepted Answer

To accurately calculate the velocity from the time the card blocks the light beam.

Question 9

A mass $$m = 0.05\ \mathrm{kg}$$ falls a height $$h = 0.4\ \mathrm{m}$$, pulling a cart of mass $$M = 0.2\ \mathrm{kg} on a $$frictionless air track. What is the final velocity $$v of $$the system? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{\frac{2mgh}{m+M}} = \sqrt{\frac{2 	imes 0.05 	imes 9.8 	imes 0.4}{0.05+0.2}} \approx 1.25\ \mathrm{m/s}$$

Question 10

Which of the following is a real-world example of an inelastic collision?

Accepted Answer

A car crash where the vehicles stick together after impact.

Question 11

If a vehicle on the air track is moving at constant velocity and passes through a light gate with an effective card length of $$0.05\ \mathrm{m}$$, and the timer records $$0.10\ \mathrm{s}$$, what is the velocity of the vehicle?

Accepted Answer

$$0.5\ \mathrm{m/s}$$

Question 12

Which of the following best describes the role of the photodiode assembly in the experiment?

Accepted Answer

It detects when the light beam is interrupted by the vehicle, allowing precise timing of motion.

Question 13

In the context of the experiment, why is it important to compare the results of momentum and kinetic energy before and after collisions?

Accepted Answer

To determine whether the collision is elastic or inelastic.

Question 14

A student finds that after an inelastic collision, the total kinetic energy is less than before the collision. What is the most likely explanation?

Accepted Answer

Some kinetic energy was converted to other forms such as heat or deformation.

Question 15

Which of the following is the correct expression for the gravitational potential energy of a mass $$m at $$height $$h$$ above the Earth's surface?

Accepted Answer

$$U_g = mgh$$

Question 16

In the experiment, why is it necessary to use a spirit level to adjust the air track?

Accepted Answer

To ensure the track is horizontal so that vehicles do not accelerate due to gravity.

Question 17

A student wants to verify the conservation of momentum in an elastic collision. Which data should they compare?

Accepted Answer

The total momentum before and after the collision.

Question 18

If friction is not negligible on the air track, what is the most likely effect on the results of the energy conservation experiment?

Accepted Answer

The measured final velocity will be less than predicted by energy conservation.

Question 19

Which of the following best describes the purpose of using plasticine as an arrestor at the end of the air track during elastic collision experiments?

Accepted Answer

To prevent the second vehicle from recoiling after the collision.

Conservation of Momentum and Energy: The Linear Air Track Experiment

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