a 2kg ball is moving rightward at 2m/s when it collides with a 6kg ball that was moving west at a speed of 4m/s. After collision the 2kg ball moves west at a speed of 4m/s. Thw 6kg ball is also moving westward after collision with a speed of 2m/s. Show momentum is conserved. Show whether or not energy is conserved. Based on your answer what type of collision do you think we have?1
I will be happy to critique your work.
To determine whether momentum is conserved, we need to calculate the momentum before and after the collision for each object involved.
The momentum of an object is calculated by multiplying its mass by its velocity.
For the 2kg ball before the collision:
Momentum = Mass × Velocity
= 2kg × 2 m/s
= 4 kg⋅m/s
For the 6kg ball before the collision:
Momentum = Mass × Velocity
= 6kg × (-4 m/s) (since it is moving westward)
= -24 kg⋅m/s
After the collision, the 2kg ball is moving westward at 4 m/s:
Momentum = Mass × Velocity
= 2kg × (-4 m/s)
= -8 kg⋅m/s
After the collision, the 6kg ball is also moving westward at 2 m/s:
Momentum = Mass × Velocity
= 6kg × (-2 m/s)
= -12 kg⋅m/s
To check if momentum is conserved, we need to add up the momentum before the collision and compare it to the total momentum after the collision.
Momentum before collision = 4 kg⋅m/s + (-24 kg⋅m/s) = -20 kg⋅m/s
Momentum after collision = (-8 kg⋅m/s) + (-12 kg⋅m/s) = -20 kg⋅m/s
The total momentum before the collision is equal to the total momentum after the collision, indicating that momentum is conserved in this system.
Now let's determine if energy is conserved. To do this, we will calculate the kinetic energy before and after the collision for each object involved.
The kinetic energy of an object is calculated by using the formula:
Kinetic Energy = 0.5 × Mass × Velocity^2
For the 2kg ball before the collision:
Kinetic Energy = 0.5 × 2kg × (2 m/s)^2
= 4 Joules
For the 6kg ball before the collision:
Kinetic Energy = 0.5 × 6kg × (-4 m/s)^2
= 48 Joules
After the collision, the kinetic energy for the 2kg ball is:
Kinetic Energy = 0.5 × 2kg × (-4 m/s)^2
= 16 Joules
After the collision, the kinetic energy for the 6kg ball is:
Kinetic Energy = 0.5 × 6kg × (-2 m/s)^2
= 12 Joules
The total kinetic energy before the collision is 4 Joules + 48 Joules = 52 Joules, while the total kinetic energy after the collision is 16 Joules + 12 Joules = 28 Joules.
Since the total kinetic energy before the collision is not equal to the total kinetic energy after the collision, energy is not conserved in this system.
Based on the fact that momentum is conserved but energy is not conserved, this collision can be classified as an inelastic collision.