Chapter 6

A pitcher accelerates a $0.14-\mathrm{kg}$ hardball from rest to $25.5\mathrm{m}/\mathrm{s}$ in $0.075\mathrm{s}$. (a) How much work does the pitcher do on the ball? (b) What is the pitcher's power output during the pitch? (c) Suppose the ball reaches $25.5\mathrm{m}/\mathrm{s}$ in less than $0.075\mathrm{s}$. Is the power produced by the pitcher in this case more than, less than, or the same as the power found in part (b)? Explain.

The average power output of the human heart is $1.33\mathrm{W}$. (a) How much energy does the heart produce in a day? (b) Compare the energy found in part (a) with the energy required to walk up a flight of stairs. Estimate the height a person could attain on a set of stairs using nothing more than the daily energy produced by the heart.

Think \& Calculate A sled slides without friction down a small, ice-covered hill. If the sled starts from rest at the top of the hill, its speed at the bottom is $7.50\mathrm{m}/\mathrm{s}$. (a) On a second run, the sled starts with a speed of $1.50\mathrm{m}/\mathrm{s}$ at the top. When it reaches the bottom of the hill, is its speed $9.00\mathrm{m}/\mathrm{s}$, more than $9.00\mathrm{m}/\mathrm{s}$, or less than $9.00\mathrm{m}/\mathrm{s}$ ? Explain. (b) Find the speed of the sled at the bottom of the hill after the second run.

A sled slides without friction down a small, ice-covered hill. If the sled starts from rest at the top of the hill, its speed at the bottom is $7.50\mathrm{m}/\mathrm{s}$. (a) On a second run, the sled starts with a speed of $1.50\mathrm{m}/\mathrm{s}$ at the top. When it reaches the bottom of the hill, is its speed $9.00\mathrm{m}/\mathrm{s}$, more than $9.00\mathrm{m}/\mathrm{s}$, or less than $9.00\mathrm{m}/\mathrm{s}$ ? Explain. (b) Find the speed of the sled at the bottom of the hill after the second run.

An $1865-\mathrm{kg}$ airplane starts at rest on an airport runway at sea level. What is the change in mechanical energy of the airplane if it climbs to a cruising altitude of $2420\mathrm{m}$ and maintains a constant speed of $96.5\mathrm{m}/\mathrm{s}$ ?

An 1865-kg airplane starts at rest on an airport runway at sea level. What is the change in mechanical energy of the airplane if it climbs to a cruising altitude of $2420\mathrm{m}$ and maintains a constant speed of $96.5\mathrm{m}/\mathrm{s}$ ?

Research and write a report on the power that humans produce in everyday life. Include the power produced by the brain when thinking and the heart when resting. Also select several strenuous activities such as trackand-field events, bicycle racing, and swimming. In each case, explain how the power is determined. Make a table to compare the various power outputs.

Connect to the Big Idea The mechanical energy of a falling ball stays the same, even though it is constantly speeding up. Similarly, if you throw a ball upward, it slows down, even though its mechanical energy stays the same. Explain.