# Mechanics: 3 Probles on conservation of energy and momentum

(See attached files for full problem descriptions with diagrams, units and proper equations)

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Let two particles of equal mass collide. Particle 1 has initial velocity , directed to the right, and particle 2 is initially stationary.

Part A

If the collision is elastic, what are the final velocities and of particles 1 and 2?

Give the velocity of particle 1 followed by the velocity of particle 2, separated by a comma. Express each velocity in terms of .

Part B

Now suppose that the collision is perfectly inelastic. What are the velocities and of the two particles after the collision?

Give the velocity of particle 1 followed by the velocity of particle 2, separated by a comma. Express the velocities in terms of .

Part C

Now assume that the mass of particle 1 is , while the mass of particle 2 remains . If the collision is elastic, what are the final velocities and of particles 1 and 2?

Give the velocity of particle 1 followed by the velocity of particle 2, separated by a comma. Express the velocities in terms of .

Part D

Let the mass of particle 1 be and the mass of particle 2 be . If the collision is perfectly inelastic, what are the velocities of the two particles after the collision?

Give the velocity of particle 1 followed by the velocity of particle 2, separated by a comma. Express the velocities in terms of .

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A bullet of mass is fired horizontally with speed at a wooden block of mass resting on a frictionless table. The bullet hits the block and becomes completely embedded within it. After the bullet has come to rest within the block, the block, with the bullet in it, is traveling at speed .

Part A

Which of the following best describes this collision?

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perfectly elastic

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partially inelastic

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perfectly inelastic

?

Part B

Which of the following quantities, if any, are conserved during this collision?

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kinetic energy only

?

momentum only

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kinetic energy and momentum

?

neither momentum nor kinetic energy

?

Part C

What is the speed of the block/bullet system after the collision?

Express your answer in terms of , , and .

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Derive using the momentum conservation and energy conservation equations:

Vf1=((m1-m2)/(m1+m2))*Vi1

And

Vf2=((2m1)/(m1+m2))*Vi1

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