A spring is hung vertically from a fixed support. When an object of mass m is at

Question

A spring is hung vertically from a fixed support. When an object of mass m is attached to the end of the spring, it stretches by a distance y. When an object of mass of 2m is hung from the spring, it stretches by a distance 2y. A second, identical spring is then attached to the free end of the first spring. If the mass 2m is attached to the bottom of the second spring, how far will the bottom of the second spring move downward from its unstretched position? Assume the masses of the springs are negligible when compared to m.

3y/2

Explanation / Answer

For first spring of mass m will stretches it y distance and if 2m is on it it will stretches to 2y distance --------(1)

For second spring , for 2m mass it will stretches to 2y distance -------------------------(2)

From (1) & (2)

The total stretch, for the combination system is 4y

So, it is 4y

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