A 5.0 kg mass hanging from a string 42 cm up in the air is dropped from rest. Ho

Question

A 5.0 kg mass hanging from a string 42 cm up in the air is dropped from rest. How fast will it be moving when it strikes the spring? What is the gravitational potential energy of the mass when the spring is at maximum compression? As the ideal spring recoils and restores, it causes the mass to bounce and relaunch upwards. How much work does the spring do on the mass in total? Explain. Is the collision of the mass with the spring elastic or inelastic? In either case identify the two objects colliding, how you know it is either elastic or inelastic, and illustrate your answer.

Explanation / Answer

Use conservation of energy,

(1/2)mv2 = mgh

so, the speed just before hitting the spring will be:

v = [2gh]1/2 = [2 x 9.8 x 0.42]1/2 = 2.87 m/s

again, use conservation of energy to find the maximum compression

at the maximum compression, the velocity is zero, therefore the kinetic energy is zero.

so, by conservation of energy, the potential energy will be: U = (5)(9.8)(0.42) = 20.58 J

Work Done by the spring = work done on the spring due to potential energy = 20.58 J.

Since the spring is ideal, the amplitude of its oscillation will be constant and so it will project the mass with the same velocity with which it initially struck the spring. Therefore, the collision will be elastic in nature (no energy loss).

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