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

**Answer 1**

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

**Answer 2**

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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…

**Answer 3**

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:

http://sharemath.com/NhX6R8So.png

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).

Source(s): Pearson University Physics for the Life Sciences textbook (2015).

**Answer 4**

Introduction To Collisions Mastering Physics

**Answer 5**

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