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CoCalc is a real-time collaborative commercial alternative to JupyterHub and Overleaf that provides Jupyter Notebooks, LaTeX documents, and SageMath.
Aaron Tresham Calculus Materials - Feb 2018 snapshot
Question 1
A spring with natural length has spring constant . How much work (in joules) is done stretching the spring to ? [Answer: 0.025 J]
Question 2
A force of is required to hold a spring that has been stretched from its natural length of to a length of . How much work (in joules) is done in stretching the spring from to . [Answer: 1.56 J]
[Hint: Remember to work in meters.]
Question 3
You have a -foot cable that weighs pounds. [Assume uniform density; that is, the cable weighs pounds/foot.]
Part a
Suppose the entire cable is rolled up on the ground next to a -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 feet and radius of 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 feet above the top of the tank ( feet above the ground). Note: Water weighs . [Answer: 351,295 ft-lbs]
[Hint: This is similar to, but easier than, Example 4, since the radius is the same at every depth.]
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