A particle is suspended from a post on top of a cart by a light string of length

Question

A particle is suspended from a post on top of a cart by a light string of length L as shown in figure [a], below. The cart and particle are initially moving to the right at constant speed vi, with the string vertical. The cart suddenly comes to rest when it runs into and sticks to a bumper as shown in figure [b], below. The suspended particle swings through an angle ? . (a) Show that the original speed of the cart can be computed from vi = 2gL(1 ? cos ?) (b) If the bumper is still exerting a horizontal force on the cart when the hanging particle is at its maximum angle forward from the vertical, at what moment does the bumper stop exerting a horizontal force? somewhere between the maximum angle forward and the lowest point of the particle the lowest point of the particle somewhere between the lowest point of the particle and the maximum angle backward the maximum angle backward never

Explanation / Answer

follow this a). at the moment the cart suddenly stop. the particle still has the velocity of Vi. so it go up the an angle of alpha conservation of energy. mv^2/2=mg*R*(1-cos alpha) so that v=sqrt(2gR(1- cos alpha)). b) the cart now is at rest, so its horizontal net force is zero. so only when the string is vertical, the force of the bumper exerte on the cart is zero.

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