A 8.5 kg steel ball, travelling left to right at 12 m/s, undergoes an elastic collision with a 5 kg steel ball at rest. To the nearest Joule, what is the Total Kinetic Energy of the two balls after collision?

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If the first ball in the question above has a mass of 10 kg and the second ball is travelling at it with a speed of 3 m/s, what is the velocity, to one decimal place, of the first ball after collision?

What is the velocity of the second ball in problem the last problem above to one decimal place?

For your first question:

In an elastic collision, the total kinetic energy does not change. In this case it equals the initial KE of the ball travelling 12/m/s.

In the second question, both momentum and total KE remain constant. You have to solve two equations in two unknowns. It gets quite messy when the masses are unequal, as in this case. You should try this exercise yourself.

There is a shortcut if you do the problem in the center-of-mass coordinate system (in which case both masses simply reverse direction at the same speed), and then transform back to laboratory coordinates.

To find the total kinetic energy of the two balls after the collision, we need to use the principle of conservation of kinetic energy. In an elastic collision, the total kinetic energy before the collision is the same as the total kinetic energy after the collision.

1) Total Kinetic Energy after collision:
The initial kinetic energy of the first ball can be calculated using the formula:
KE1 = 1/2 * m1 * v1^2,
where m1 is the mass of the first ball (8.5 kg) and v1 is the velocity of the first ball before the collision (12 m/s).

The initial kinetic energy of the second ball is:
KE2 = 1/2 * m2 * v2^2,
where m2 is the mass of the second ball (5 kg) and v2 is the velocity of the second ball before the collision (which is at rest, so v2 = 0 m/s).

Therefore, the total initial kinetic energy before the collision is:
Total KE = KE1 + KE2.

Now, since this is an elastic collision, the total kinetic energy after the collision will be the same as the total kinetic energy before the collision:
Total KE (after collision) = Total KE (before collision).

2) Velocity of the first ball after collision:
To find the velocity of the first ball after the collision, we can use the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is the same as the total momentum after the collision.

The initial momentum of the first ball is given by:
P1_initial = m1 * v1,
where P1_initial is the initial momentum of the first ball, m1 is the mass of the first ball (8.5 kg), and v1 is the velocity of the first ball before the collision (12 m/s).

The initial momentum of the second ball is given by:
P2_initial = m2 * v2,
where P2_initial is the initial momentum of the second ball, m2 is the mass of the second ball (5 kg), and v2 is the velocity of the second ball before the collision (3 m/s).

Therefore, the total initial momentum before the collision is:
Total P_initial = P1_initial + P2_initial.

Again, since this is an elastic collision, the total momentum after the collision will be the same as the total momentum before the collision:
Total P_final = Total P_initial.

To find the velocity of the first ball after collision, we can rearrange the equation:
Total P_final = m1 * v1_final + m2 * v2_final,
where v1_final is the velocity of the first ball after the collision (which we are looking for), and v2_final is the velocity of the second ball after the collision.

To solve for the velocity of the first ball after collision, we can rearrange the equation and substitute the known values, such as the mass of the second ball (5 kg), the initial velocity of the second ball (3 m/s), and the calculated values of the total initial momentum and the velocity of the first ball before the collision.