Question #3217

A block of mass M, at rest on a horizontal, frictionless surface, is attached to a rigid support by a spring of force constant k. A bullet of mass m and velocity v strikes the block and remains embedded in the block. Determine, a.) the velocity of the block immediately after the collision and b.) the amplitude of the resulting simple harmonic motion.

Expert's answer

To find the velocity of the block immediately after the collision we can use the law of conservation of linear momentum:

Where p

According to the definition of linear momentum:

Where v

And p

So

Answer:

To find the amplitude of the resulting simple harmonic motion we can use the law of conservation of energy:

E

Potential energy of the spring is

Where x is displacement of the block;

Amplitude is maximum displacement so

Block is in frictionless surface so the law of conservation of energy can be written as:

So

Answer :

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