A pool ball of mass 100g and velocity [5,-4]m/s collides with a stationary pool ball of the same mass. After the collision, the pool balls have velocites [2,-3]m/s and [3,-1]m/s. Is the collision elastic? Explain your answer.
Lets check energy
before: 1/2 .1 * (25+16)=
2.05 joules
after= 1/2 .1*(4+9)+1/2 .1(9+1)
=1/2 (1.3)+1/2 (1)=1/2 (2.3) not elastic. Energy is lost
I have not response
A pool ball of mass 100g velocity 4-5
Well, I hate to burst your bubble, but it seems like this collision is not elastic. How do I know that? Well, because I have eyes, well, metaphorical eyes, and I can see that the velocities of the pool balls have changed after the collision.
In an elastic collision, there would be no change in the total kinetic energy of the system. But in this case, the velocities have definitely changed, indicating that the kinetic energy has also changed. It's like someone sneaking into a magic show and replacing the disappearing rabbit with a turtle. It's just not the same!
So, to sum it up, based on the changes in velocity and kinetic energy, this collision is as elastic as a rubber chicken trying to hula hoop – which is to say, not elastic at all!
To determine whether the collision is elastic or not, we need to check if both the momentum and kinetic energy are conserved.
1. Firstly, let's calculate the initial momentum and the final momentum of the system:
- Initial momentum = mass × velocity
- Momentum of the first pool ball (before collision):
Mass = 100g = 0.1kg
Initial velocity = [5,-4] m/s
Initial momentum = 0.1kg × [5, -4] = [0.5, -0.4] kg·m/s
- Momentum of the second pool ball (before collision):
Since it is stationary, its momentum will be zero.
- Total initial momentum = Initial momentum of first ball + Initial momentum of second ball
= [0.5, -0.4] kg·m/s + [0, 0] kg·m/s
= [0.5, -0.4] kg·m/s
- Final momentum = mass × velocity
- Momentum of the first pool ball (after collision):
Final velocity = [2, -3] m/s
Final momentum = 0.1kg × [2, -3] = [0.2, -0.3] kg·m/s
- Momentum of the second pool ball (after collision):
Final velocity = [3, -1] m/s
Final momentum = 0.1kg × [3, -1] = [0.3, -0.1] kg·m/s
- Total final momentum = Final momentum of first ball + Final momentum of second ball
= [0.2, -0.3] kg·m/s + [0.3, -0.1] kg·m/s
= [0.5, -0.4] kg·m/s
2. Secondly, let's calculate the initial kinetic energy and the final kinetic energy of the system:
- Initial kinetic energy = 0.5 × mass × velocity^2
- Initial kinetic energy of the first pool ball:
Initial velocity = [5, -4] m/s
Initial kinetic energy = 0.5 × 0.1kg × (5^2 + (-4)^2) m^2/s^2 = 0.5J
- Initial kinetic energy of the second pool ball:
Since it is stationary, its initial kinetic energy is zero.
- Total initial kinetic energy = Initial kinetic energy of first ball + Initial kinetic energy of second ball
= 0.5J + 0J = 0.5J
- Final kinetic energy = 0.5 × mass × velocity^2
- Final kinetic energy of the first pool ball:
Final velocity = [2, -3] m/s
Final kinetic energy = 0.5 × 0.1kg × (2^2 + (-3)^2) m^2/s^2 = 0.385J
- Final kinetic energy of the second pool ball:
Final velocity = [3, -1] m/s
Final kinetic energy = 0.5 × 0.1kg × (3^2 + (-1)^2) m^2/s^2 = 0.29J
- Total final kinetic energy = Final kinetic energy of first ball + Final kinetic energy of second ball
= 0.385J + 0.29J = 0.675J
Now, to determine if the collision is elastic:
- If the momentum is conserved, the final momentum should be equal to the initial momentum:
[0.5, -0.4] kg·m/s = [0.5, -0.4] kg·m/s
- If the kinetic energy is conserved, the final kinetic energy should be equal to the initial kinetic energy:
0.675J ≠ 0.5J
Since the final kinetic energy is not equal to the initial kinetic energy, the collision is NOT elastic.