92. In Figure P5.92, the pulleys and the cord are light, all surfaces are fricti

Question

92. In Figure P5.92, the pulleys and the cord are light, all surfaces are frictionless, and the cord does not stretch. (a) How does the acceleration of block I compare with the acceleration of block 2? Explain your reasoning. (b) The mass of block 2 is 1.30 kg. Find its acceleration as it depends on the mass m1 of block 1. (c) What If? What does the result of part (b) predict if m1 is very much less than 1.30 kg? (d) What does the result of part (b) predict if m1 approaches infinity? (e) In this last case, what is the tension in the cord? (f) Could you anticipate the answers to parts (c), (d), and (e) without first doing part (b)? Explain.

Explanation / Answer

a) Here , for the block 1 and block 2 ,

let the acceleration of block 1 is a1

acceleration of block 2 is a2 ,

a1 = 2 * a2

b)

let the tension in the string is T ,

m1 * a1 = T

and

1.3 * 9.8 - 2T = 1.3 * a2

12.74 - 2*m1 * a2/2 = 1.3 * a2

a2 = 12.74 / (m1 + 1.3)

the acceleration of block 2 is 12.74 / (m1 + 1.3)

c)

for very small m1

a2 = 12.74/1.3

a2 = 9.8 m/s^2

d) for very large m1 ,

a2 = 0 m/s^2

e) for the infinite mass ,

2*T = 1.3 * 9.8

T = 6.37 N

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