Answer to Question #304812 in Physics for mmm

Question

In raising a 5000-N piano with a pulley system, the workers note that for every 2m or rope pulled down, the piano rise 0.4m.

A. ideally, how much force is required to lift the piano?

B. if the workers actually pull with 2500N of force to lift the piano, what is the efficiency of the pulley system?

Answer 1

a) Since no energy is produced by the pulley, the works should be equal:

$$F_1d_1 = F_2d_2$$

where $d_1 = 2m,d_2=0.4m$ are the displacement of the rope and piano, and $F_1, F_2 = 5000N$ are corresponding forces. Thus, obtain:

$$F_1 = \dfrac{F_2d_2}{d_1} = \dfrac{5000N\cdot 0.4m}{2m} = 1000N$$

b) The efficiency is the ratio of obtained and applied work:

$$\eta = \dfrac{F_2d_2}{F_1d_1} \times100\%= \dfrac{5000N\cdot 0.4m}{2500N\cdot 2m}\times100\% = 40\%$$

Answer. a) 1000N, b) 40%