First slide

Two block problem

Question

A block A of mass 100 kg rests on another block B of mass 200 kg and is tied to a wall as shown in the figure. The coefficient of friction between A and B is 0.2 and that between B and the ground is 0.3. The minimum force F required to move the block B is (Take, 9 = 10 $m s^{- 2}$ )

Moderate

A

900 N
B

200 N
C

1100 N
D

700 N

Solution

Friction force between block A and block B; and between block B and surface will oppose the force F.
$∴$ $F = F_{A B} + F_{B S}$
$= μ_{A B} m_{A} g + μ_{B S} (m_{A} + m_{B}) g$
$= 0.2 \times 100 \times 10 + 0.3 (100 + 200) 10$
$= 200 + 900 = 1100 N$
This is the required minimum force to move the block B.

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