Calculating Final Speed in Elastic collision (momentum)

[Mushroom79]

Homework Statement

If it is eg. two balls, both going to the right before and after an elastic shock, how do you determine their velocities after the collision? (speeds before and weights are given)

Eg.

M = 50 kg
u1 = 20 m / sm = 100 kg
v1 = 10 m / s

(M, m = mass)
(u1, v1 = velocity before the collision)
(u2, v2 = velocity after collision)

Homework Equations

The law of conservation of momentum:
m*v1+M*u1= m+M*v2*u2

Momentum before = Momentum after

The Attempt at a Solution

m*v1+M*u1= m+M*v2*u2 →

100 * 10 +50 * 20 = 100 +50 * v2 * u2

How do I continue from here?

 

[ZxcvbnM2000]

In elastic collisions energy is also conserved , so you can set up one more equation .

 

[Mushroom79]

In elastic collisions energy is also conserved , so you can set up one more equation .

Oh, right. Think "momentum before equals momentum after" is what you meant.
Forgot to put it there.

 

[ZxcvbnM2000]

In elastic collisions :

Momentum is conserved

Energy Is conserved
In inelastic collisions:

Momentum Is conserved

Energy is not conserved

Just to be more clear :P

 

[asteriatic]

To determine the velocities after the collision, you can use the equations for conservation of momentum and conservation of kinetic energy. The equation for conservation of momentum is:

m1*u1 + m2*u2 = m1*v1 + m2*v2

where m1 and m2 are the masses of the objects, u1 and u2 are the initial velocities, and v1 and v2 are the final velocities.

To solve for v2, you can rearrange the equation to get:

v2 = (m1*u1 + m2*u2 - m1*v1) / m2

You can also use the equation for conservation of kinetic energy, which states that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. This can be written as:

1/2 * m1 * u1^2 + 1/2 * m2 * u2^2 = 1/2 * m1 * v1^2 + 1/2 * m2 * v2^2

To solve for v2, you can rearrange the equation to get:

v2 = sqrt((m1*u1^2 + m2*u2^2 - m1*v1^2) / m2)

Using either of these equations, you can calculate the final velocities of the objects after the elastic collision. Remember to use the correct units for mass (kg) and velocity (m/s) in your calculations.