Ball of mass 450g lands on a spring with k = 5.0E3

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A ball of mass 450g lands on a spring with k = 5.0E3 . The ball was originally dropped from a height of 2.50 m. Determine the maximum compression of the spring AND the velocity it will leave with after bouncing of the spring.

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Let F[/f]be the force exerted by the falling ball of mass m on the spring with spring constant k. Since the ball is under free fall, the force wih which the ball falls on the spring is its weight mg. Hence,

mg=-kx, where xis the displacement of the spring.
Therefore, x=mg/k. After the spring has been compressed, force generated is transferred to the ball. Thus the Potential energy of the spring is converted to the kinetic energy of the ball.

Thus,
1/2*k2 = 1/2*m*v2

Find out the velocity of ball using the above equation.


Sridhar
 

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