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Let two objects of equal mass m collide. Object 1 has initial velocity v , direc

ID: 2257897 • Letter: L

Question

Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary.

A. If the collision is perfectly elastic, what are the final velocities v1 and v2 of objects 1 and 2?

Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express each velocity in terms of v.

B. Now suppose that the collision is perfectly inelastic. What are the velocitiesv1 and v2 of the two objects after the collision?

Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express each velocity in terms of v.

C. Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m. If the collision is elastic, what are the final velocities

v1 and v2 of objects 1 and 2?

Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express each velocity in terms of v.

D. Let the mass of object 1 be m and the mass of object 2 be 3m. If the collision is perfectly inelastic, what are the velocities of the two objects after the collision?

Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express each velocity in terms of v.



Explanation / Answer

1. For an elastic head-on (assumed) collision between equal masses, they simply swap velocities. The final velocities of objects 1 and 2 are 0 and v, respectively.


2. mv = (2m)u

where u = final velocity. Then u = v1 = v2 = v/2


3. Initially, p = (2m)v

final p = 2mv = 2mv1 + mv2

But for an elastic head-on collision, we know that the

relative velocity of approach = relative velocity of separation, or

v = v2 - v1

v2 = v + v1

plug into final p:

2mv = 2mv1 + m(v + v1) = 2mv1 + mv + mv1

mv = 3mv1

v1 = v/3

v2 = v + v/3 = 4v/3


4. initial p = mv

final p = mv = (m + 3m)u = 4mu

u = v1 = v2 = v/4