A small block of mass 20 kg rests on a bigger block of mass 30 kg, which lies on a smooth horizontal plane. Initially the whole system is at rest. The coefficient of friction between the blocks is 0.5. The horizontal force, F=50 N, is applied on the lower block. The work done by frictional force on upper block in t=2 s is n × 10 J. Find n.

Question

A small block of mass 20 kg rests on a bigger block of mass 30 kg, which lies on a smooth horizontal plane. Initially the whole system is at rest. The coefficient of friction between the blocks is 0.5. The horizontal force, F=50 N, is applied on the lower block. The work done by frictional force on upper block in t=2 s is n × 10 J. Find n. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Assuming both Block are moving together

a = \frac{50}{50} = 1 m / s^{2}

f = 20 \times 1 = 20 N

f_{L} = 0.5 \times 20 \times 10

\Rightarrow 100 N

f_{required} = 20 N

which is less than

F_{L}

so block move together

S_{upper} = \frac{1}{2} \times 1 \times 2^{2} = 2

metre

f = 20 N

W = 20 \times 2 = 40

Joule

Assuming both Block are moving together a=5050​=1m/s2 f=20×1=20N fL​=0.5×20×10 ⇒100N frequired ​=20N which is less than FL​ so block move together Supper ​=21​×1×22=2 metre f=20N W=20×2=40 Joule