A block of mass m is on top of a block of mass M = 4 m . The two blocks are conn

Question

A block of mass m is on top of a block of mass M = 4m. The two blocks are connected by a string that passes over an ideal pulley. The bottom block is also tied to a string - exerting a force F, after the blocks have been set in motion, causes the blocks to move at constant velocity.

Use g = 10 N/kg for this problem. The coefficient of kinetic friction between all surfaces in contact is 0.100.

(a) For this scenario, which free-body diagrams (see above) are correct? Select the two correct diagrams, one for each block, and make sure you can identify which force is which.

The correct free-body diagram of the larger block is number 1.

The correct free-body diagram of the larger block is number 2.

The correct free-body diagram of the larger block is number 3.

The correct free-body diagram of the smaller block is number 4.

The correct free-body diagram of the smaller block is number 5.

The correct free-body diagram of the smaller block is number 6.

(b) If the value of m is 120 g, what is the value of F?
____ N

Explanation / Answer

given, block of mass m on the top of another block of mass M connected by string
let tension in the string be T
M = 4m
Foce on bottom block = F
coefficient of kinetic fricion, k = 0.1

so, the bottom block will have force F acting towards left, Weight acting downwards, Normal rection due to the ground to the top, Normla reaction due to the top b lock , downwards, and frcition due to the two surfaces and the tension in the string to the right
so Diagram 1 depicts Block M

Block m, will have friciton to left, Tension to right and normal / weight pair
so opiton 4 is block m

so the answer is The correct free-body diagram of the larger block is number 1.
The correct free-body diagram of the smaller block is number 4.

as the blocks are moving with constnat speed
k*m*g = T
and
F = T + k*m*g + k*5m*g = 6kmg + T
F = 7kmg
m = 0.12 kg
F = 7*0.1*0.12*9.81 = 0.824 N

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