Work AP Physics C Mechanics FRQ – Exam Style Questions etc.
Work AP Physics C Mechanics FRQ
Unit 3: Work, Energy, and Power
Weightage : 15-25%
Question
A uniform chain of mass M and length l hangs from a hook in the ceiling. The bottom link is now raised vertically and hung on the hook as shown above on the right.
a. Determine the increase in gravitational potential energy of the chain by considering the change in position of the center of mass of the chain.
b. Write an equation for the upward external force F(y) required to lift the chain slowly as a function of the vertical distance y.
c. Find the work done on the chain by direct integration of ∫ 𝐹𝑑𝑦.
Answer/Explanation
Ans:
a. using the ceiling as a reference point: Ui = – ½ mgl; Uf = – ¼ mgl
∆U = Uf – Ui = ¼ mgl
b. 
λ = m/l, the weight of the piece being held is λsg = mgs/l; s = y/2 so F(y) = mgy/2l
c. \(\int_{0}^{l}Fdy = \frac{mg}{2l}\int_{0}^{l}ydy = \frac{mg}{2l}\frac{l^{2}}{2}= \frac{1}{4}mgl\)