Max Height of m1 After Elastic Collision on Frictionless Track

In summary, two blocks, one with a mass of 5 kg and the other with a mass of 10 kg, are on a frictionless wooden track. The first block is released from a height of 5 meters and has a north pole magnet on its front end. The second block has an identical magnet embedded in its back end and is initially at rest. The two blocks never touch. Using conservation of energy and balancing momentum and kinetic energy, we can calculate the maximum height that the first block will rise to after the elastic collision. However, there may be missing information or a diagram needed to fully solve the problem.
  • #1
chevyboy86
15
0
Two blocks are free to slide along a frictionless wooden track. A block of mass m1=5 kg is released from point A. Protruding from its front end is the north pole of a strong magnet, repelling the north pole of an identical magnet embedded in the back end of the block of mass m2=10 kg, initially at rest. The two blocks never touch. Calculate the maximum height to which m1 rises after the elastic collsion.

m1 is initially at a height of 5 meters. I don't know what equation to use for this problem.
 
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  • #2
Assume convservation of energy.

Balance momentum before and after impact.
Balance kinetic energy before and after impact.
 
  • #3
There must be some sort of diagram that goes with this? I believe there is information missing here.

Edit: Though I guess if you work to make the problem meaningful, conservation of energy will make most other information unnecessary.
 
  • #4
Yeh, I would figure that it is a (vertically) circular track, since m1 has a height and the question asks for a final height.
 

1. What is the formula for calculating the maximum height of M1 after an elastic collision on a frictionless track?

The formula for calculating the maximum height of M1 after an elastic collision on a frictionless track is:
h = (m1/m2 + 1) * v12 / 2g
where h is the maximum height, m1 and m2 are the masses of the two objects, v1 is the initial velocity of M1, and g is the gravitational acceleration.

2. How does the mass of M1 affect the maximum height after an elastic collision on a frictionless track?

The mass of M1 has a direct impact on the maximum height after an elastic collision on a frictionless track. The higher the mass of M1, the lower the maximum height will be. This is because a heavier object will have a lower velocity after the collision, resulting in a lower maximum height reached.

3. What is the significance of a frictionless track in this scenario?

A frictionless track is significant in this scenario because it eliminates the loss of kinetic energy due to friction. This allows for a more accurate calculation of the maximum height reached by M1 after the collision. In real-life scenarios, friction would cause the objects to lose some of their energy, resulting in a lower maximum height.

4. Can the maximum height of M1 after an elastic collision on a frictionless track ever be greater than its initial height?

No, the maximum height of M1 after an elastic collision on a frictionless track can never be greater than its initial height. This is because the gravitational force will always act against the motion of the object, causing it to eventually come to a stop and fall back down. The maximum height reached will always be lower than the initial height.

5. How does the angle of collision between M1 and M2 affect the maximum height reached by M1?

The angle of collision between M1 and M2 does not have a direct effect on the maximum height reached by M1. However, it can affect the velocity of M1 after the collision, which in turn can affect the maximum height reached. The angle of collision can also impact the direction in which M1 travels after the collision, which may affect the maximum height reached depending on the shape of the track.

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