A bob suspended from the ceiling of a car which is accelerating on a horizontal road. The bob stays at rest with respect to the car with the string making an angle e with the vertical. The linear momentum of the bob as seen from the road is increasing with time. Is it a violation of conservation of linear momentum? If not, where is the external force which changes the linear momentum?

Question

Philoid · Accepted Answer

Let the acceleration of the car be ‘a’. The forces on the bob from the frame of reference of the car is shown in the above picture.

Since there is no motion in the vertical direction we can say,

or, .

In horizontal direction, on applying Newton’s second law we get,

where a’ is the acceleration of the bob in the horizontal direction

with respect to the ground frame. So, we can see that there is a

net non-zero force in the horizontal direction which is responsible

for the acceleration observed.

So, there is no violation of the law of conservation of momentum.