# Let two objects of equal mass (m) Object 1 has an initial velocity (v) to the right, object 2 is stationary?

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

2. Now suppose that the collision is perfectly inelastic. What are the velocities v1 and v2 of the two objects after the collision?

3.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?

4.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?

Any help (and explanation) would be greatly appreciated

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

• Linnell

RE:

Let two objects of equal mass (m) Object 1 has an initial velocity (v) to the right, object 2 is stationary?

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

2. Now suppose that the collision is perfectly inelastic. What are the velocities v1 and v2 of the two objects after the collision?

3.Now assume that the mass of object 1 is (2m) , while the…

• Erika

Use these equations (image links below) are for the perfectly inelastic collision questions.

They originate from the composition of the conservation of momentum and conservation of kinetic energy equations.

Note: They only work when OBJECT 2 is initially at rest (v=0 at t=0). Velocity can be in the x or y direction but not both (separate all multidirectional components).

Final velocity of object 1:

http://sharemath.com/vFV84eJA.png

Final velocity of object 2:

http://sharemath.com/mxQQXrQ6.png

For the PERFECTLY inelastic collisions:

Use this equation which uses the fact that both objects have the same final velocities since they are “stuck” together (inelastic, means moving object didn t bounce off stationary object, in this instance).

• John

Introduction To Collisions Mastering Physics

• scarlethunt

1). v1, v2 = 0, v 2). v/2, v/2 3).v/3, 4v/3 4). v/4, v/4

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