Question

a child of mass 35 kg is sitting on a trolley of mass 5kg the trolley is given a push by applying a force so that it begins to move with a speed of 4m/s the trolley comes to rest after covering a distance of 16m. fin i) the work done on the trolley ii) the work done by the trolley before coming to rest

Answer 1

Total mass of the trolley=40 kg

Distance covered before coming to rest=16 m

It is given a force so that it moves with a speed or velocity=4m/s

In the question there are two cases

Work done on the trolley.

Work done by the trolley before coming to rest

Since retardation of the trolley is

16/32=0.5m/s^-2

Since the trolley is given a push therefore work done by the force there fore net friction force acting on the trolley ios equal to 40*0.5=20 Newton

Therefore Intital Kinetic Energy of the trolley=320 J

Final kinetic energy of the trolley=0 Joules

therefore work done =320 Joules

320 Joules is the work done by the trolley i mean the net force which acts on the trolley

now

Applied force by the push can be calculated as

x-20/40=0.5

=0.5*40=x-20

20=x-20

20+20=x

40=x

therefore applied force=40 Newtons

therefore

Work done on the trolley=40*16=640 Newtons



Note here that work done by the trolley is equal to the work done by the net force on the trolley. Work done on the the trolley is equal to the force applied*displacement.