Two hockey pucks with a mass of 0.1 kg slide across the ice and collide. Before the collision puck 1 is going 8 m/s to the east and puck two is Going 7 m/s to the west. After the collision puck one is going 7 m/s to the west. What is the velocity of puck two
letting east by +, we conserve momentum and end up with
0.1(8) + 0.1(-7) = 0.1(-7) + 0.1v
clearly, v = +8
To find the velocity of puck two after the collision, we need to first determine the velocity change of puck one and use it to find the velocity change of puck two.
1. Determine the velocity change of puck one:
- Initial velocity of puck one (before collision): 8 m/s to the east
- Final velocity of puck one (after collision): 7 m/s to the west
- Velocity change of puck one = Final velocity - Initial velocity
- Velocity change of puck one = 7 m/s (west) - 8 m/s (east)
- Velocity change of puck one = -1 m/s (west)
2. Apply the principle of conservation of momentum:
- According to the principle of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
- Momentum is calculated by multiplying mass and velocity.
- Before the collision:
- Puck one momentum = mass of puck one * initial velocity of puck one
- Puck one momentum = 0.1 kg * 8 m/s (east)
- Puck one momentum = 0.8 kg·m/s (east)
- Puck two momentum = mass of puck two * initial velocity of puck two
- Puck two momentum = 0.1 kg * -7 m/s (west)
- Puck two momentum = -0.7 kg·m/s (west)
- Total momentum before the collision = Puck one momentum + Puck two momentum
- Total momentum before the collision = 0.8 kg·m/s (east) + (-0.7 kg·m/s) (west)
- Total momentum before the collision = (0.8 - 0.7) kg·m/s
- Total momentum before the collision = 0.1 kg·m/s (east)
- After the collision:
- Puck one momentum = mass of puck one * final velocity of puck one
- Puck one momentum = 0.1 kg * 7 m/s (west)
- Puck one momentum = -0.7 kg·m/s (west)
- Puck two momentum = mass of puck two * final velocity of puck two
- Puck two momentum = 0.1 kg * final velocity of puck two (unknown)
- Total momentum after the collision = Puck one momentum (from above) + Puck two momentum (unknown)
- Total momentum after the collision = -0.7 kg·m/s (west) + 0.1 kg·m/s (unknown)
3. Equate the total momentum before the collision to the total momentum after the collision:
- 0.1 kg·m/s (east) = -0.7 kg·m/s (west) + 0.1 kg·m/s (unknown)
- 0.1 kg·m/s (east) = -0.6 kg·m/s (west) + 0.1 kg·m/s (unknown)
- 0.1 kg·m/s (east) + 0.6 kg·m/s (west) = 0.1 kg·m/s (unknown)
- 0.7 kg·m/s = 0.1 kg·m/s (unknown)
4. Solve for the unknown (final velocity of puck two):
- 0.1 kg·m/s (unknown) = 0.7 kg·m/s
- unknown = 0.7 kg·m/s ÷ 0.1 kg
- unknown = 7 m/s to the east
Therefore, the final velocity of puck two after the collision is 7 m/s to the east.
To find the velocity of puck two after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can write the equation for the conservation of momentum as:
(mass of puck 1 * velocity of puck 1 before collision) + (mass of puck 2 * velocity of puck 2 before collision) = (mass of puck 1 * velocity of puck 1 after collision) + (mass of puck 2 * velocity of puck 2 after collision)
Substituting the given values:
(0.1 kg * 8 m/s) + (0.1 kg * (-7 m/s)) = (0.1 kg * (-7 m/s)) + (0.1 kg * velocity of puck 2 after collision)
Now we can solve for the velocity of puck two after the collision.
0.8 kg m/s - 0.7 kg m/s = -0.7 kg m/s + 0.1 kg * velocity of puck 2 after collision
0.1 kg * velocity of puck 2 after collision = -0.1 kg m/s
velocity of puck 2 after collision = -1 m/s
Therefore, the velocity of puck two after the collision is 1 m/s to the west.