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Chapter 9: Q. 37 (page 229)

a. How much work must you do to push a 10kg block of steel across a steel table at a steady speed of 1.0m/s for 3.0s?

b. What is your power output while doing so?

Short Answer

Expert verified

a). work done is 176.4J

b). power output is58.8W

Step by step solution

01

Step 1. Part a). Find the work done

Work done on block is W=F鈭�r, where we don't know (yet) force or displacement. If we look at force on block, we see that there are two on block: friction and force of push. We can use second law of Newton

ma鈫�=鈭�F鈫�0=Ffriction-FpushFpush=mg渭steeltosteel=10kg路9.8m/s2路0.6=58.8

Displacement with velocity and elapsed time

鈭�r=v鈭�t=1m/s路3=3m

So, work required to push the block is

W=F鈭�r=58.8N路3m=176.4J

02

Step 2. Part b). Power Output

P=鈭�W鈭�tP=176.43P=58.8

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Most popular questions from this chapter

You need to raise a heavy block by pulling it with a massless rope. You can either (a) pull the block straight up height h, or (b) pull it up a long, frictionless plane inclined at a 15o angle until its height has increased by h. Assume you will move the block at constant speed either way. Will you do more work in case a or case b? Or is the work the same in both cases? Explain.

A 90kg firefighter needs to climb the stairs of a 20m-tall building while carrying a 40kg backpack filled with gear. How much power does he need to reach the top in 55s?

An 8.0kg crate is pulled 5.0m up a 30掳incline by a rope angled 18掳above the incline. The tension in the rope is 120N, and the crate鈥檚 coefficient of kinetic friction on the incline is 0.25.

a. How much work is done by tension, by gravity, and by the normal force?

b. What is the increase in thermal energy of the crate and incline?

Hooke鈥檚 law describes an ideal spring. Many real springs are better described by the restoring force (Fsp)s=-k鈭�s-q(鈭�s)3, where q is a constant.

Consider a spring with k=250N/m .

It is alsoq=800N/m3.

a. How much work must you do to compress this spring 15cm? Note that, by Newton鈥檚 third law, the work you do on the spring is the negative of the work done by the spring.

b. By what percent has the cubic term increased the work over what would be needed to compress an ideal spring? Hint: Let the spring lie along the s-axis with the equilibrium position of the end of the spring at s=0.

Then 鈭唖 = s.

If a particle鈥檚 speed increases by a factor of 3, by what factor does its kinetic energy change?
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