Two ice skaters, with masses of 75 kg and 55 kg, stand facing each other, glide backward straight toward the river's edges, and reach the edges at exactly the same time. How far did the 75 kg skater glide?

Two ice skaters, with masses of 50 kg and 75 kg, are at the center of a 60-m-diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier skater reaches the edge in 20 s, how long does the lighter skater take to reach the edge?

Two skaters, one with mass 65 kg and the other with mass 40 kg, stand on an ice rink holding a pole of length 10 m and negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they meet. How far does the 40 kg skater move?

Ethan, whose mass is 80 kg, stands at one end of a very long, stationary wheeled cart has a mass of 500 kg. He then starts sprinting toward the other end of the cart. He soon reaches his top speed of 8.0 m/s, measured relative to the cart. What is the speed of the cart when Ethan has reached his top speed?

The two ropes seen in Figure metioned are used to lower a $255 \mathrm{~kg}$ piano $5.00 \mathrm{~m}$ from a second-story window to the ground. How much work is done by each of the three forces?

Two ice skaters stand at rest in the center of an ice rink. When they push off against each other, the 45-kg skater acquires a speed of 0.62 m/s. If the speed of the other skater is 0.89 m/s, what is that skater's mass?

At the center of a 50 -m-diameter circular ice rink, a $75 \mathrm{~kg}$ skater traveling north at $2.5 \mathrm{~m} / \mathrm{s}$ collides with and holds on to a $60 \mathrm{~kg}$ skater who had been heading west at $3.5 \mathrm{~m} / \mathrm{s}$. a. How long will it take them to glide to the edge of the rink? b. Where will they reach it? Give your answer as an angle north of west.

A 2.7 kg block of wood sits on a frictionless table. A 3.0 g bullet, fired horizontally at a speed of 500 m/s, goes completely through the block, emerging at a speed of 220 m/s. What is the speed of the block immediately after the bullet exits?

In 1831, soldiers marched across the Broughton Bridge in England in "lock step"-that is, marching in time together. As they marched, the bridge began to bounce in time with their footsteps; the amplitude of this bouncing became larger and larger until the bridge suddenly collapsed. Explain why the lockstep of the soldiers caused this collapse and why afterward soldiers were ordered to "break step," or march at their own individual rates, as they crossed bridges.

What is the angular momentum of the $2.0 \mathrm{~kg}, 4.0-\mathrm{cm}$-diameter rotating disk in Fiugre mentioned?

A 20 g ball of clay is thrown horizontally at 30 m/s toward a 1.0 kg block sitting at rest on a frictionless surface. The clay hits and sticks to the block. a. What is the speed of the block and clay right after the collision? b. Use the block's initial and final speeds to calculate the impulse the clay exerts on the block. c. Use the clay's initial and final speeds to calculate the impulse the block exerts on the clay. d. Does $\vec { J } _ { \text { block onclay } } = - \vec { J } _ { \text { clay on block } }$?

A 2.0 kg block slides along a frictionless surface at 1.0 m/s. A second block, sliding at a faster 4.0 m/s, collides with the first from behind and sticks to it. The final velocity of the combined blocks is 2.0 m/s. What was the mass of the second block?

The $670\text{ g}$ bar is rotating as shown in the figure. What is the angular momentum of the bar about the axle? Express your answer with the appropriate units.

As we discussed earlier shows the operation of a garlic press. The lower part of the press is held steady, and the upper handle is pushed down, thereby crushing a garlic clove through a screen. Approximate distances are shown in the figure. If the user exerts a $12 \mathrm{~N}$ force on the upper handle, estimate the force on the clove.