A particle is suspended fro m a post on top of a cart by a light string of lengt

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 ? .

(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?

2gL(1 ? cos ?) 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? . Show that the original speed of the cart can be computed from vi = 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

a) conservation of energy

Ei = Ef

1/2 mv^2 = m g h

but h = L - L cos theta

so 1/2 mv^2 = m g L ( 1- cos theta)

solve for v

v = sqrt( 2 g L( 1- cos theta))

b) the lowest point of the particle
since then the x component of the tension will switch directions

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