Question

Consider a cart pushed along a track with a certain force, if the force remains the same while the mass of the cart decreases to half, the acceleration of the cart ______.

Answer 1

Doubles (under the assumption there is no friction between the cart and the track)

Step-by-step explanation:

The acceleration produced by a force, F, on a mass, m, is given by

`a =(F)/(m)`

It is seen that, when the force is constant, the acceleration is inversely proportional to the mass.

Thus, if the mass is halved,

`a_n =(F)/(0.5m)= 2(F)/(0.5m) = 2a`

The acceleration is doubled.

However, if there's friction between the track and the cart, the reduction of the mass reduces friction between. While the applied force remains constant, the effective force increases. The acceleration will then depend additionally on the values of the coefficients of friction and the applied force.