Question

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 θ 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 changes the linear momentum?

Answer 1

No, there is no linear momentum’s violation of conservation. The external force is the car’s friction force which is acting via the suspended bob’s string. It is the tension force in the string, the module of which the linear momentum in horizontal direction changes.

Explanation:

• The car’s acceleration be ‘a’. From the reference frame of the car, the bob’s forces are displayed.

• As in the vertical direction, there is no motion, it can be said that  $T \cos (e)-m g=0$ or $T \cos (e)=m g.$
• Applying the second law of Newton in the horizontal direction, we obtain, $T \sin (e)=m a^{\prime}$.
• Here, in the horizontal direction, the bob’s direction has the acceleration denoted as ‘a’. It can be observed that in the horizontal direction, there is a net non-zero force that is responsible for the observed acceleration.  
• Thus, it can be concluded that there is no violation for the law of momentum’s conservation.