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 (see the dashed lines in the diagram). If he chooses 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 which path, if either, does the professor does less work? Hint: Think about the connection between work and potential energy (in cases where the object gains no kinetic energy).

Explanation / Answer

A) The professor might not apply the force parallel to the plane B) The professor might lift the cart somewhat higher than the table when placing the cart on the table C) PE = m g h so the increase in potential energy is the same in both cases.

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