Question

A block of mass 1 kg is horizontally thrown with a velocity of 10 m/s on a stationary long plank of
mass 2 kg whose surface has u = 0.5. Plank rests on frictionless surface. Find the time when block
comes to rest w.r.t. plank.
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Answer 1

initial velocity of block w.r.t plank , u = 10m/s²

body comes to rest w.r.t plank so, final velocity of block w.r.t plank , v = 0

here frictional force is acting between contacting surface of block and plank

regarding force = frictional force

or, ma = umg

or, a = ug = 0.5 × 10 = 5m/s² , this is acceleration of block when plank is in rest.

but because frictional force is also acting on plank so, it also moves,

again, Ma = umg

or, a = umg/M = 0.5 × 1 × 10/2 = 5/2 m/s² [ opposite directions of motion of block ]

now, relative acceleration = 5 + 5/2 = 15/2

now applying formula , v = u + at

or, 0 = 10 + (-15/2) t

or, 10 = 15/2 t

or, 4/3 = t

hence, time taken by block comes to rest w.r.t plank is 4/3

Answer 2

Answer :-

F = v dm/dt

= 5 x 1

= 5N

acceleration= a = F/m

= 5/2

= 2.5 ms⁻²