Work Assignment.sagews

Work Assignment

Question 0

Watch the lecture video here.

Did you watch the video? [Type yes or no.]

Question 1

A spring with natural length $0.1\ m$ has spring constant $k=5\ N/m$. How much work (in joules) is done stretching the spring to $0.2\ m$? [Answer: 0.025 J]

Question 2

A force of $40\ N$ is required to hold a spring that has been stretched from its natural length of $10\ cm$ to a length of $15\ cm$. How much work (in joules) is done in stretching the spring from $15\ cm$ to $18\ cm$. [Answer: 1.56 J]

[Hint: Remember to work in meters.]

Question 3

You have a $100$-foot cable that weighs $300$ pounds. [Assume uniform density; that is, the cable weighs $\frac{300}{100}=3$ pounds/foot.]

Part a

Suppose the entire cable is rolled up on the ground next to a $100$-foot building. How much work (in ft-lbs) is required to bring the entire cable to the roof of the building? [Answer: 30,000 ft-lbs]

[Hint: No integral is required, since the whole weight is lifted the entire distance.]

Part b

Suppose the cable is hanging from the top of the building to the ground. How much work (in ft-lbs) is required to pull the entire cable to the roof? [Answer: 15,000 ft-lbs]

Part c

Why is the work less in part b than in part a?

Question 4

A cylindrical water tank with depth of $4$ feet and radius of $8$ feet has one circular base on the ground. If the tank is full, how much work (in ft-lbs) is required to pump all the water in the tank $5$ feet above the top of the tank ($9$ feet above the ground). Note: Water weighs $62.4\text{ lbs/ft}^3$. [Answer: 351,295 ft-lbs]

[Hint: This is similar to, but easier than, Example 4, since the radius is the same at every depth.]

This material was developed by Aaron Tresham at the University of Hawaii at Hilo and is
licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.