A lazy professor wants to lift a cart from the floor onto a table. He can either

Question

A lazy professor wants to lift a cart from the floor onto a table. He can either lift it straight up along path 1, or he can push it up the ramp along path 2, the cart rolls with negligible friction. Whichever path he chooses, the cart starts at rest on the floor and ends at rest on the table. Here's the issue. Along which path will the professor do less work on the cart?

a. Why might a smart student say the professor does less work lifting the cart along path 1.

b. Why might a smart student say the professor does less work pushing the cart along path 2

c. Along with path, if either, does the professor do less work?

d. Reconcile your answer with part c answer with the arguments guven in Part A or B. In other words, show how elements of the incorrect ideas from part A or Part B can be used to correctly explain why your part C answers makes intuitive sense.

Explanation / Answer

a. one might say that because the professor has to go a farther distance, he does more work.
b. one might say that pushing an object up a ramp is easier than lifting it.
c. The professor does the same amount of work with each path. the only distance that matters is the height. In each case, the change in height is the same so the work done is the same.
D. The first student is wrong because even tho the professor goes farther, he is still lifting it the same height as if he decided to simply lift it. The second student is wrong because even though it is easier to go up an incline, he has to travel farther, and the change in height ends up being the same as if he had decided to just lift it. Either way, the professor is covering the same vertical distance which is all that mattters

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