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.

Consider a ballistic pendulum (see Section 7.6) in which a bullet strikes a block of wood. The wooden block is hanging from the ceiling and swings up to a maximum height after the bullet strikes it. Typically, the bullet becomes embedded in the block. Given the same bullet, the same initial bullet speed, and the same block, would the maximum height of the block change if the bullet did not get stopped by the block but passed through to the other side? Would the height change if the bullet and its speed were the same but the block was steel and the bullet bounced off it, directly backward?

A bullet with a mass of $4.0 \mathrm{~g}$ and a speed of $650 \mathrm{~m} / \mathrm{s}$ is fired at a block of wood with a mass of $0.095 \mathrm{~kg}$. The block rests on a frictionless surface, and is thin enough that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is $23 \mathrm{~m} / \mathrm{s}$. What is the speed of the bullet when it exits the block?

The mass of Earth is $5.97 \times 10^{24} \mathrm{~kg}$ and its orbital radius is an average of $1.50 \times 10^{11} \mathrm{~m}$. Calculate the magnitude of its linear momentum at the location in the

A skater of mass 40 kg is carrying a box of mass 5 kg. The skater has a speed of 5 m/s with respect to the floor and is gliding without any friction on a smooth surface. a. Find the momentum of the box with respect to the floor. b. Find the momentum of the box with respect to the floor after she puts the box down on the frictionless skating surface.

Two friends stand on rollerskates, facing each other within arm's reach. Jimi pushes gently on his friend Tony's upraised palms. What happens?
A Jimi remains motionless and Tony rolls backward.
B. Jimi rolls backward and Tony remains motionless.
C. Jimi rolls forward and Tony rolls backward.
D. Jimi and Tony each roll backward.

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 $15,000 \mathrm{~kg}$ rocket traveling at $+230 \mathrm{~m} / \mathrm{s}$ turns on its engines. Over a $6.0 \mathrm{~s}$ period it burns $1,000 \mathrm{~kg}$ of fuel. An observer on the ground measures the velocity of the expelled gases to be $-1,200 \mathrm{~m} / \mathrm{s}$.
a What is the resulting speed of the rocket after the burn?
b. What is the acceleration of the rocket during the burn? Express your answer in meters per second squared and in " $g$s.
c. What impulse is applied to the rocket?

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?

The $12 -\mathrm{ft}$ boom $AB$ has a fixed end $A$, and the tension in cable $B C$ is $570 \mathrm{~lb}$. Replace the force that the cable exerts at $B$ by an equivalent force-couple system at $A$.

The 12 - $\mathrm{ft}$ boom AB has a fixed end A. A steel cable is stretched from the free end B of the boom to a point $C$ located on the vertical wall. If the tension in the cable is $380 \mathrm{lb}$, determine the moment about $A$ of the force exerted by the cable at $B$.

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?