Describe two different scenarios where the same object has identical momentum.

Two clouds collide and form another, more massive cloud. One cloud is stationary, while the other is traveling at $1 \mathrm{~m} / \mathrm{s}$. After the collision, the new, combined cloud travels with a velocity of $0.25 \mathrm{~m} / \mathrm{s}$. What is the ratio of the masses of the two original clouds?

In an elastic collision involving two balls where one is stationary before the collision, can you make any generalizations about the speed and direction of the two balls after the collision? Consider the situations where (a) the moving ball is more massive than the stationary one; (b) the stationary ball is more massive than the moving ball, and (c) the two balls have equal masses.

If In an elastic collision, a $1.0 \mathrm{~kg}$ ball moving at $1.0 \mathrm{~m} / \mathrm{s}$ collides with a $2.0 \mathrm{~kg}$ ball moving at $-2.0 \mathrm{~m} / \mathrm{s}$. The $2.0 \mathrm{~kg}$ ball transfers all of its momenta to the $1.0 \mathrm{~kg}$ ball.
a. What velocity does the $1.0 \mathrm{~kg}$ ball have after the collision?
b. What is the initial kinetic energy of the system?
c. What is the final kinetic energy of the system?

A stationary $165 \mathrm{~kg}$ football player is tackled by a $178 \mathrm{~kg}$ player running at $8 \mathrm{~m} / \mathrm{s}$
a. How fast are they moving after the collision?
b. What is the impulse imparted on the stationary player?
c. What is the impulse imparted on the moving player?

A $2,000 \mathrm{~kg}$ car moving at $10 \mathrm{~m} / \mathrm{s}$ collides head-on with a $2,500 \mathrm{~kg}$ car moving in the opposite direction at $15 \mathrm{~m} / \mathrm{s}$. The two cars are locked together after impact.
a. Is this an elastic or an inelastic collision? Why?
b. What is the speed of the cars after impact?
c. Calculate the kinetic energies of the cars, both before and after impact.
d. What fraction of the kinetic energy was lost during the impact? Where did the energy go?

If A $2.0 \mathrm{~kg}$ puck is moving east at $5.5 \mathrm{~m} / \mathrm{s}$. It catches up to and collides with a second identical puck moving due east at $3.0 \mathrm{~m} / \mathrm{s}$. The collision is perfectly inelastic.

a. What is the resulting velocity of the pucks?
b. What is the initial kinetic energy $E_{k i}$ of the system?
c. What is the change in kinetic energy, $\Delta E_k$, of the system as a result of the collision?
d. If the mass $m$ is doubled, but the initial velocities are unchanged, does the resulting velocity increase, decrease, or remain unchanged?

A $10,000 \mathrm{~kg}$ railroad car traveling north at $10 \mathrm{~m} / \mathrm{s}$ collides with a $5,000 \mathrm{~kg}$ rail car also moving north but at an unknown speed. After the collision, the two cars lock together and move north at $8 \mathrm{~m} / \mathrm{s}$. How fast was the second car moving before the impact?

A $1,200 \mathrm{~kg}$ car is heading due north at $14.0 \mathrm{~m} / \mathrm{s}$. It collides with an identical car heading due south at $14.0 \mathrm{~m} / \mathrm{s}$. What is the combined momentum of the cars before the collision?

A collision where the objects stick together after impact is called a/an

Two carts connected with a compressed spring are placed somewhere along a frictionless track of $4.0 \mathrm{~m}$ in length. One cart has a mass of $150 \mathrm{~g}$, and the heavier cart has a mass of $275 \mathrm{~g}$. The spring is released and the two carts move off toward the two ends of the track, reaching the ends at the same instant.
a. Which cart is initially closer to its end of the track, the light cart or the heavy cart?
b. If the heavy cart gains a velocity of $2.0 \mathrm{~m} / \mathrm{s}$, what is the velocity of the light cart?
c. How far from its end of the track is the heavy cart placed initially?
d. How much momentum is produced by the release of the spring?
e. How much kinetic energy is produced by the release of the spring?
f. Energy is always conserved. Where does the kinetic energy of the carts come from?
g. If the compression of the spring is increased, which of these answers a- $\mathrm{f}$ will change?

Calculate the recoil (backward momentum) and velocity of a $4.0 \mathrm{~kg}$ rifle that fires a $20 \mathrm{~g}$ bullet that travels $1.0 \mathrm{~m}$ in $2.15 \times 10^{-3} \mathrm{~s}$.

A ball with a mass of $0.5 \mathrm{~kg}$ is traveling at $25 \mathrm{~m} / \mathrm{s}$ and collides with a ball at rest that has a mass of $2 \mathrm{~kg}$. After the collision, both balls are traveling $5 \mathrm{~m} / \mathrm{s}$ in the same direction. Was momentum conserved?

A car and an attached trailer have a combined mass of $3,000 \mathrm{~kg}$. The car and trailer are moving on the highway at a velocity of $25 \mathrm{~m} / \mathrm{s}$. After going over a small bump in the road, the trailer detaches from the car. If the car's speed after separation is $27 \mathrm{~m} / \mathrm{s}$ and its final momentum is $35,000 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$, what are the masses of the car and trailer, respectively?