First slide

Two block problem

Question

A 40 kg slab rests on a frictionless floor as shown in the figure. A l0 kg block rests on the top of the slab. The static coefficient of friction between the block and slab is 0.60 while the kinetic friction is 0.40. The l0 kg block is acted upon by a horizontal force 100 N. If g = 9.8 $m / s^{2}$ , the resulting acceleration of the slab will be

Moderate

A

1 $m / s^{2}$
B

1.5 $m / s^{2}$
C

2 $m / s^{2}$
D

6 $m / s^{2}$

Solution

Limiting friction between block and slab - $μ_{s} m_{A} g$ = 0.6 x 10 x l0=60N
But applied force on block I is 100 N. So the block will slip over a slab.
Now kinetic friction works between block and slab
$F_{K}$ = $μ_{k} m_{A} g$ = 0.4 x l0 x l0 = 40 N
This kinetic friction helps to move the slab
Acceleration of slab = $\frac{40}{m_{B}} = \frac{40}{40} = 1 m / s^{2}$

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