Question 1

Two astronauts, A and B, are floating in space and push off from each other as shown in the first image. If astronaut A has twice the mass of astronaut B, which of the following statements is correct about their velocities immediately after the push?

Accepted Answer

Astronaut B will move away with twice the velocity of astronaut A.

Question 2

In the ice skater scenario (second image), why is the total momentum of the system conserved even though external forces like gravity and the normal force act on the skaters?

Accepted Answer

Because the external forces are equal and opposite, their vector sum is zero.

Question 3

A curling stone of mass $$m$$ slides with velocity $$v_{1,i} = 1.50 m/s $$and collides elastically with an identical stone at rest (see third image). After the collision, the first stone moves at $$v_{1,f} = 0.610 m/s at$$ $$66.08^{\circ}$$ from the original direction. What is the speed of the second stone after the collision?

Accepted Answer

$$v_{2,f} = 1.37 m/s$$

Question 4

Why do high jumpers use the 'Fosbury flop' technique as shown in the fourth image?

Accepted Answer

It allows the jumper to clear the bar with a lower center of mass trajectory.

Question 5

For a uniform solid sphere, where is the center of mass located?

Accepted Answer

At the geometric center of the sphere.

Question 6

A wrench is thrown in the air and spins as shown in the sixth image. What path does the center of mass of the wrench follow?

Accepted Answer

A straight line, regardless of the rotation of the wrench.

Question 7

After a shell explodes in midair (seventh image), what happens to the center of mass of the system?

Accepted Answer

It continues to follow the original parabolic trajectory.

Question 8

In a star-planet system (eighth image), what does the 'cm' point represent?

Accepted Answer

The center of mass of the star-planet system.

Question 9

A rocket of mass $$m$$ ejects a small amount of fuel $$dm at $$exhaust velocity $$v_{ex} ($$ninth image). What is the correct differential equation for the rocket's velocity?

Accepted Answer

$$m dv = -v_{ex} dm$$

Question 10

Which of the following best describes the action-reaction forces between two ice skaters pushing off each other (second image)?

Accepted Answer

The force skater A exerts on skater B is equal in magnitude and opposite in direction to the force skater B exerts on skater A.

Question 11

If a donut-shaped object has a uniform density, where is its center of mass located (see fifth image)?

Accepted Answer

At the geometric center of the hole, which is not within the material of the donut.

Question 12

A shell explodes in midair, breaking into two fragments. If the shell was moving horizontally before the explosion, what can be said about the horizontal velocity of the center of mass after the explosion?

Accepted Answer

It remains the same as before the explosion.

Question 13

A rocket is launched vertically upward. If the exhaust velocity is $$v_{ex}$$ and the initial mass is $$m_0$$, what is the rocket's velocity after burning fuel to reach mass $$m ($$ignoring gravity)?

Accepted Answer

$$v = v_0$ - v_{ex} \ln\left(\frac{m_0$}{m}\right)$$

Question 14

Which of the following is true about the center of mass of a system of particles?

Accepted Answer

It moves as if all the external forces were applied to a single particle of mass equal to the total mass of the system.

Question 15

If a system is isolated and no external forces act on it, what can be said about its total momentum?

Accepted Answer

The total momentum is conserved.

Question 16

A solid cone of height $$h$$ and uniform density has its center of mass located at what height from the base?

Accepted Answer

$$z_{cm} = \frac{3h}{4}$$

Question 17

In the context of rocket propulsion, what is the physical meaning of the exhaust velocity $$v_{ex}$$?

Accepted Answer

It is the velocity of the ejected fuel relative to the rocket.

Momentum, Impulse, and Collisions: Principles and Applications

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