Let two objects of equal mass collide. Object 1 has initial velocity , directed

Question

Let two objects of equal mass collide. Object 1 has initial velocity , directed to the right, and object 2 is initially stationary.
1. If the collision is perfectly elastic, what are the final velocities and of objects 1 and 2?
2. Now suppose that the collision is perfectly inelastic. What are the velocities and of the two objects after the collision?
3.
Now assume that the mass of object 1 is , while the mass of object 2 remains . If the collision is elastic, what are the final velocities and of objects 1 and 2?
4. Let the mass of object 1 be and the mass of object 2 be . If the collision is perfectly inelastic, what are the velocities of the two objects after the collision?

Explanation / Answer

A.Conservation of momentum can be used IF there no external forcesacting on it
derive an equation to fit v1 and v2

mv1 + mv2 = mv
equal mass leaving v
mv1^2 + mv^2 = mv^2
equal mass; eliminate m

0, v

B. Perfectly inelastic means that they are equal. Use the sameequations for part A

v/2, v/2

C. Elastic allows you to write different equations

we have 2mv1 + mv2 = 2mv
m factors out
v1^2 + mv2^2 = (2m)v^2
factor out m

v/3, 4 * v/3

D. Just like part B

using equation mv1 + 3mv2 = mv

They will be equal

v/4, v/4

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