Question

A small block B is placed on another block A of mass 5 kg and length 20 cm. Initially, the block B is near the right end of block A (Figure 5−E3). A constant horizontal force of 10 N is applied to the block A. All the surfaces are assumed frictionless. Find the time that elapses before block B separates from A.

Figure

Answer 1

Mass of block A, m = 5 kg
F = ma = 10 N
$\Rightarrow a=\frac{10}{5}=2\mathrm{m}/{\mathrm{s}}^2$
As there is no friction between A and B, when block A moves, block B remains at rest in its position.

Initial velocity of A, u = 0
Distance covered by A to separate out,
s = 0.2 m
Using $s=ut+\frac{1}{2}a{t}^2$, we get:
$0.2=0+\frac{1}{2}\times 2t^2$
⇒ t² = 0.2
⇒ t = 0.44 s ≈ 0.45 s