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A ball of mass 5 kg is suspended from a cord of length L = 0.5 m is attached to a cart A of mass 25 kg which slides freely on a frictionless horizontal track as shown in figure. The ball is given an initial horizontal velocity 1 m/s while cart is at rest. Find(a) The velocity of the ball when string makesmaximum angle with vertical.(b The maximum vertical distance h throughwhich the ball will rise.

Alvin Carter , 6 Years ago

Grade 12

1 Answers

Eshan

Last Activity: 6 Years ago

Dear student,

The ball will make the maximum angle with vertical when it comes to rest with respect to the cart. Thus, the speed of both cart and ball must be same and in the horizontal direction. Let it be $v$ .

Hence from conservation of linear momentum along the horizontal direction,

$mv_0=(M+m)v\implies v=\dfrac{5}{25+5}\times 1m/s=\dfrac{1}{6}m/s$

Also from conservation of energy,

$\dfrac{1}{2}mv_0^2=mgh+\dfrac{1}{2}mv^2+\dfrac{1}{2}Mv^2$

$\implies h=\dfrac{1}{24}m$

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