Q: A 60 kg archer stands on a frictionless surface and fires a 0.05 kg arrow at 50 m/s horizontally. What is the archer's recoil velocity immediately after firing?

$$v_{archer} = -0.042 \text{ m/s}$$

Question 1

A baseball player hits a ball with a bat, causing the ball to change direction rapidly. Which concept best explains the large change in the ball's momentum during the collision?

Accepted Answer

Impulse, which is the product of the average force and the time interval over which the force acts: $$I = \overline{F} \Delta t$$

Question 2

A cart of mass $$m is at $$rest on a frictionless track. A person standing on the cart throws a ball of mass $$m_b$$ horizontally forward. What happens to the cart after the ball is thrown?

Accepted Answer

The cart moves backward due to conservation of momentum.

Question 3

Which of the following is the correct vector equation for the linear momentum $$\vec{p} of a $$particle with mass $$m$$ and velocity $$\vec{v}$$?

Accepted Answer

$$\vec{p} = m \vec{v}$$

Question 4

A 60 kg archer stands on a frictionless surface and fires a 0.05 kg arrow at 50 m/s horizontally. What is the archer's recoil velocity immediately after firing?

Accepted Answer

$$v_{archer} = -0.042 	ext{ m/s}$$

Question 5

Which statement about collisions is correct?

Accepted Answer

Momentum is conserved in all collisions, regardless of whether kinetic energy is conserved.

Question 6

Two carts, one of mass $$m$$ and the other of mass $$2m$$, are at rest on an air track. You push each cart with the same constant force for the same amount of time. What is the ratio of the final momentum of the light cart to the heavy cart?

Accepted Answer

The ratio is 1:1; both carts have equal momentum.

Question 7

A ball moving at speed $$v is $$brought to rest (case i). The same ball is pushed from rest so that it moves at speed $$v ($$case ii). The same ball moving at speed $$v is $$brought to rest and then pushed backward to its original speed (case iii). In which case does the ball undergo the largest change in momentum?

Accepted Answer

Case (iii)

Question 8

Which of the following best describes a perfectly inelastic collision?

Accepted Answer

The colliding objects stick together after the collision and move with a common velocity.

Question 9

A car of mass $$m$$ collides with a wall and comes to rest. If the initial velocity of the car is $$v_0$$ and the collision lasts $$\Delta t$$, what is the magnitude of the average force exerted by the wall on the car?

Accepted Answer

$$F_{avg} = \frac{m v_0$}{\Delta t}$$

Question 10

Which of the following is true about elastic collisions?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 11

During a collision, the force between two objects varies with time. The impulse delivered to one object is equal to:

Accepted Answer

The area under the force vs. time curve: $$I = \int_{t_i}^{t_f} F_{ext} dt$$

Question 12

A proton collides elastically with a stationary $$^4He $$nucleus. Which of the following statements is correct?

Accepted Answer

Both momentum and kinetic energy are conserved in the collision.

Question 13

Which equation expresses Newton's Second Law in terms of momentum?

Accepted Answer

$$\sum \vec{F} = \frac{d\vec{p}}{dt}$$

Question 14

In a regular inelastic collision, which of the following is true?

Accepted Answer

Some kinetic energy is lost, but the objects do not stick together.

Question 15

A ball of mass $$m$$ moving at velocity $$v$$ collides head-on elastically with a stationary ball of equal mass. What are their velocities after the collision?

Accepted Answer

The moving ball comes to rest, and the stationary ball moves with velocity $$v.$$

Question 16

Which of the following is a correct statement about the impulse-momentum theorem?

Accepted Answer

The change in momentum of an object equals the impulse applied: $$\Delta p = I$$

Question 17

Two ice skaters, one of mass $$m$$ and the other of mass $$2m$$, push off against each other on frictionless ice. If the lighter skater moves away with velocity $$v$$, what is the velocity of the heavier skater?

Accepted Answer

$$v_{heavy} = -\frac{m}{2m} v = -\frac{v}{2}$$

Question 18

A ball of mass $$m is $$dropped from height $$h$$ and bounces off the ground with the same speed it had just before impact. If the contact time with the ground is $$\Delta t$$, what is the magnitude of the average force exerted by the ground on the ball?

Accepted Answer

$$F_{avg} = \frac{2 m v}{\Delta t}$$, where $$v = \sqrt{2gh}$$

Question 19

In a ballistic pendulum experiment, a bullet of mass $$m is $$fired into a block of mass $$M$$ suspended from a string. The bullet embeds in the block, and the combined system swings upward. Which principle is used to determine the initial speed of the bullet?

Accepted Answer

Conservation of momentum during the collision, followed by conservation of energy during the swing.

Linear Momentum, Impulse, and Collisions: Study Notes

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