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Block on a Block Problems

In the figure...

Question

In the figure below, masses $m_{A} = 2 k g$ and $m_{B} = 4 k g$ . For what minimum value of $F$ , block A starts slipping over B $(g = 10 m / s^{2})$

24 N

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36 N

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12 N

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20 N

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Solution

The correct option is B $36 N$
FBD of block A and B,
Maximum frictional force between A and B,
$f_{1} = μ_{1} m_{A} g = (0.2 \times 2 \times 10) N$
$f_{1} = 4 N$
Acceleration, $a = \frac{f_{1}}{m_{A}} = \frac{4}{2} = 2 m / s^{2}$
Now, taking (A+B) as the system,
$(f_{2})_{m a x} = μ_{2} (m_{A} + m_{B}) g = 24 N$
$F - 24 = (m_{A} + m_{B}) a = 6 \times 2 = 12$
$∴ F = 36 N$

The correct option is (B)

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In the figure below, masses mA=2 kg and mB=4 kg. For what minimum value of F, block A starts slipping over B (g=10 m/s2)

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