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Spring Energy Question

A block of mass M on a horizontal frictionless table is connected to a spring (constant k). The block is at the left and attached to an horizontal spring , and the right end of the spring is itself attached to the wall. The block is set in motion so that it oscillates about its equilibrium point with a certain amplitude Ao. The period of motion is To=2*pi*sqrt(M/k)

A lump of sticky putty of mass m is dropped onto the block. The putty sticks without bouncing. The putty hits M at the instant when M has its maximum velocity. Find:
(1) The new period
(2) The new amplitude
(3) The change in the mechanical energy of the system

Solution Preview

When all the energy of spring is converted to kinetic energy...

(1/2)k(Ao)^2 = (1/2)Mv^2

You can solve this for v

v = Ao*sqrt(k/M)

This will be the largest velocity.

Now then we drop a piece of putty on the block and the putty sticks. Immediately that tells me to use conservation of momentum and NOT conservation of energy.

so I will call (v1) the ...

Solution Summary

When all the energy of spring is converted to kinetic energy, we can use the formula (1/2)k(Ao)^2 = (1/2)Mv^2 to solve for the largest velocity: v = Ao*sqrt(k/M).