A 110 g block on a frictionless table is firmly attached to one end of a spring

Question

A 110 g block on a frictionless table is firmly attached to one end of a spring with k = 27 N/m . The other end of the spring is anchored to the wall. A 24 g ball is thrown horizontally toward the block with a speed of 5.5 m/s .

A-If the collision is perfectly elastic, what is the ball's speed immediately after the collision?

B-What is the maximum compression of the spring?

C-Repeat part A for the case of a perfectly inelastic collision.

D-Repeat part B for the case of a perfectly inelastic collision.

Explanation / Answer

given,

mass of block = 110 g

k = 27 N/m

mass of ball = 24 g

speed = 5.5 m/s

by conservation of momentum

initial momentum = final momentum

0.024 * 5.5 = 0.024 * v1 + 0.11 * v2

by conservation of energy

initial energy = final energy

0.5 * 0.024 * 5.5^2 = 0.5 * 0.024 * v1^2 + 0.5 * 0.11 * v2^2

on solving we'll get

ball's speed immediately after the collision v1 = -3.52985 m/s

0.5 * kx^2 = 0.5 * mv^2

0.5 * 27 * x^2 = 0.5 * 0.024 * 5.5^2

maximum compression of the spring x = 0.16397 m

in case of inelastic collision

0.024 * 5.5 = (0.024 + 0.11) * v

ball's speed immediately after the collision v = 0.985 m/s

0.5 * 27 * x^2 = 0.5 *(0.024 + 0.11) * 0.985^2

maximum compression of the spring x = 0.06939 m

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