# 3) Two carts are in contact on a horizontal frictionless surface. Cart 'A' has a mass of 3 kg, and cart 'B' a mass of 2 kg. (a) Find the force F on 'A' needed to give the two carts an acceleration of 0.8 m/sec2 . What is then the force exerted on 'B' by 'A'? (b) If the carts are given an equal acceleration in the opposite direction by pushing on B, find the force exerted on 'A' by 'B'. Explain why the force exerted on 'B' by 'A' in part (a) is not equal to the force exerted by 'A' on 'B' in part (b).

1
by rajusetu

2014-12-30T15:24:27+05:30

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A)

Force needed to give both carts acceleration of 0.8 m/sec/sec
F  = (3+2) 0.8 = 4 N
Force exerted on B by A is = 2 * 0.8 = 1.6 N

b)
I suppose there is no force F (as in part (a) acting on A.  There is only a force acting on B in the opposite direction.

force exerted by B on A  is = mass of A * acceleration = 3 * 0.8 = 2.4 N
in the opposite direction

c)
since accelerations are same , forces are different,. The reason is the difference in mass or  INERTIA.

F = m a    =>  Force is proportional mass.  Or,  higher force is needed to give the same acceleration to an object of higher mass.