A ball with a mass of #5 kg # and velocity of #8 m/s# collides with a second ball with a mass of #2 kg# and velocity of #- 6 m/s#. If #10%# of the kinetic energy is lost, what are the final velocities of the balls?

Question

A ball with a mass of #5 kg # and velocity of #8  m/s# collides with a second ball with a mass of #2 kg# and velocity of #-  6 m/s#. If #10%# of the kinetic energy is lost, what are the final velocities of the balls?

Julia Aguilar · Accepted Answer

See below.

I have explained in detail two different versions of this problem today. Here is a link to one of those explanations. Please feel free to comment here or send me a message if you need further assistance.

Carson Alexander · Answer

undefined To solve for the final velocities of the balls after the collision, you can use the principle of conservation of momentum and kinetic energy. After the collision, the total momentum and total kinetic energy of the system remain constant. Using these principles and the given information, you can calculate the final velocities of the balls. Here's how to do it:

1. First, calculate the initial momentum of the system using the formula:
   Initial momentum = (mass of first ball × velocity of first ball) + (mass of second ball × velocity of second ball)

2. Next, calculate the initial kinetic energy of the system using the formula:
   Initial kinetic energy = 0.5 × (mass of first ball × (velocity of first ball)^2) + 0.5 × (mass of second ball × (velocity of second ball)^2)

3. Since 10% of the kinetic energy is lost, calculate the amount of kinetic energy lost:
   Kinetic energy lost = 0.1 × Initial kinetic energy

4. Subtract the kinetic energy lost from the initial kinetic energy to find the final kinetic energy:
   Final kinetic energy = Initial kinetic energy - Kinetic energy lost

5. Now, use the principle of conservation of momentum to find the final velocities of the balls. Set up the equations:
   Total momentum before collision = Total momentum after collision
   (mass of first ball × velocity of first ball) + (mass of second ball × velocity of second ball) = (mass of first ball × final velocity of first ball) + (mass of second ball × final velocity of second ball)

6. Solve the equations simultaneously to find the final velocities of the balls.

Using these steps, you can determine the final velocities of the balls after the collision.