Q: A 0.5 kg cart moving at 2 m/s collides with a 0.3 kg cart moving at -2 m/s on a frictionless track. After the collision, the 0.3 kg cart moves at 2 m/s. What is the velocity of the 0.5 kg cart after the collision?

$$v_{a,2} = \frac{(0.5 \times 2) + (0.3 \times -2) - (0.3 \times 2)}{0.5} = -2.4\,\mathrm{m/s}$$

Question 1

A 0.5 kg ball moving horizontally at 30 m/s is stopped by a constant force over 20 ms. What is the magnitude of the impulse delivered to the ball?

Accepted Answer

$$J = (0.5\,\mathrm{kg})(30\,\mathrm{m/s}) = 15\,\mathrm{kg\cdot m/s}$$

Question 2

Which of the following best describes the impulse-momentum theorem?

Accepted Answer

$$\vec{J}_{\mathrm{tot}} = \Delta \vec{p} = \vec{F}_{\mathrm{net}} \Delta t$$

Question 3

A rifle of mass 3.00 kg fires a 5.00 g bullet horizontally at 300 m/s. What is the recoil velocity of the rifle?

Accepted Answer

$$v_{\mathrm{rifle}} = -\frac{m_{\mathrm{bullet}} v_{\mathrm{bullet}}}{m_{\mathrm{rifle}}} = -\frac{0.005 	imes 300}{3.00} = -0.5\,\mathrm{m/s}$$

Question 4

In a collision between two objects on a frictionless surface, which condition must be met for the total momentum of the system to be conserved?

Accepted Answer

The vector sum of the external forces on the system must be zero.

Question 5

A 0.5 kg cart moving at 2 m/s collides with a 0.3 kg cart moving at -2 m/s on a frictionless track. After the collision, the 0.3 kg cart moves at 2 m/s. What is the velocity of the 0.5 kg cart after the collision?

Accepted Answer

$$v_{a,2} = \frac{(0.5 	imes 2) + (0.3 	imes -2) - (0.3 	imes 2)}{0.5} = -2.4\,\mathrm{m/s}$$

Question 6

Which of the following statements about elastic and inelastic collisions is correct?

Accepted Answer

In an elastic collision, both momentum and kinetic energy are conserved.

Question 7

A ballistic pendulum consists of a block of mass $$M$$ and a bullet of mass $$m. $$The bullet is fired into the block and they stick together. If the combined mass swings upward to a height $$h$$, what was the initial speed $$v of $$the bullet?

Accepted Answer

$$v = \frac{M + m}{m} \sqrt{2gh}$$

Question 8

A 2.0 kg object has kinetic energy 2.0 J, a 2.0 kg object has kinetic energy 4.0 J, a 3.0 kg object has kinetic energy 3.0 J, and a 1.0 kg object has kinetic energy 7.0 J. Rank the objects in order of their momentum, from largest to smallest.

Accepted Answer

4, 2, 3, 1

Question 9

A person loosely holds a rifle and fires a bullet. What is true about the momenta of the rifle and bullet after firing?

Accepted Answer

They have equal magnitude and opposite direction.

Question 10

A girl walks from the front to the back of a canoe on a still lake. What happens to the canoe?

Accepted Answer

The canoe will still be at rest, but it will be south of its original position.

Question 11

Two carts are placed on a horizontal air track. The mass of the first cart is $$m$$ and the mass of the second cart is $$1.5m. $$The first cart is accelerated to a speed $$v$$ just before it collides with the second cart at rest. What is the speed of the center of mass of the system containing the two carts after the collision?

Accepted Answer

$$v_{\mathrm{cm}} = \frac{m v}{2.5m} = 0.4v$$

Question 12

A 200 kg block is moving to the right at 6.00 m/s on a frictionless surface. A 100 kg block is at rest. What is the velocity of the center of mass of the two blocks?

Accepted Answer

$$v_{\mathrm{cm}} = \frac{200 	imes 6.00 + 100 	imes 0}{200 + 100} = 4.00\,\mathrm{m/s}$$

Question 13

A 0.1 kg particle is at rest at $$x = 8.0 m on $$the x-axis. The center of mass of a two-particle system is at $$x = 2.0 m. $$What is the mass of the other particle located at the origin?

Accepted Answer

$$m_1 = 0.3$$\,\mathrm{kg}$$

Question 14

Which of the following is the correct vector equation for the momentum of a system of $$N$$ particles?

Accepted Answer

$$\vec{P} = \sum_{i=1}^{N} m_i \vec{v}_i$$

Question 15

A shell is fired and explodes in midair, breaking into two fragments. What happens to the center of mass of the system after the explosion?

Accepted Answer

It continues along the same trajectory as before the explosion.

Question 16

Two ice hockey players, one 60 kg and one 80 kg, are at opposite ends of a 10 m pole on frictionless ice. If they pull themselves together, how far does the 60 kg player move before they meet?

Accepted Answer

$$d = \frac{80}{60 + 80} 	imes 10 = 5.71\,\mathrm{m}$$

Question 17

Which of the following is the correct expression for kinetic energy in terms of momentum?

Accepted Answer

$$K = \frac{p^2$}{2m}$$

Question 18

A car crashes into a wall and comes to a stop, or crashes into a tub of gelatin and comes to a stop. In both cases, what can be said about the total impulse on the car?

Accepted Answer

The total impulse is the same in both cases.

CH8-EXAM-2-Momentum, Impulse, and Conservation: Study Notes for Physics

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