Answer to Question #269528 in Mechanics | Relativity for Bushra

Question

1. Block 1 of mass m1 = 2 kg is placed on block 2 of mass m2 = 3 kg which is then placed on

a table. A string connecting block 2 to a hanging mass M passes over a pulley attached to one

end of the table, as shown in Fig. 1. The mass and friction of the pulley are negligible. The

coefficients of friction between block 1 and block 2 are /1s = 0.2, M1k = 0.1 and between block

2 and the tabletop are 42s = 0.3, Mzk = 0.15.

(a) Draw the complete free body diagram of the system and determine the largest

value of M for which the blocks can remain at rest.

(b)Now suppose that M

= 2.5 kg which is large enough so that the hanging block

descends and block 1 slips on block 2. Draw the complete free body diagram of the system and

determine each of the followings.

I. The magnitude a of the acceleration of block 1

it. The magnitude ay of the acceleration of block 2

Answer 1

The maximum friction force on the blocks on the table is f2max = µs2N2 = µs2(m1 + m2)g which is balanced by the weight of the hanging mass: Mg = µs2(m1 + m2)g giving M = µs2(m1 + m2)