Elastic Collision of Blocks on a Half-Pipe: How to Determine the Final Heights?

In summary, the blocks rise to different heights depending on where along the flat section they collide.
  • #1
fightboy
25
0
Two blocks are released from rest on either side of a frictionless
half-pipe. Block B is more massive than
block A. The height HB from which block B is released is less
than HA, the height from which block A is released. The blocks
collide elastically on the flat section. After the collision, which
is correct?
A. Block A rises to a height greater than HA and block B
rises to a height less than HB.
B. Block A rises to a height less than HA and block B
rises to a height greater than HB.
C. Block A rises to height HA and block B rises to
height HB.
D. Block A rises to height HB and block B rises to
height HA.
E. The heights to which the blocks rise depends on where
along the flat section they collide.
I honestly didn't understand where to start with this problem, and got confused on the solution walkthrough. It basically wrote out two equations based on the conservation of momentum and conservation of energy, which said could be used to calculate the final speeds and then the final heights. Is there a more intuitive, less complicated way of figuring out this problem or does it require multiple equations? If someone could kindly give me an explanation for this problem it would be much appreciated!
 
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  • #2
Well we can't really give you an explanation, that would be doing your homework for you. Conservation of energy and momentum are good places to start, do you know why?
 
  • #3
BiGyElLoWhAt said:
Well we can't really give you an explanation, that would be doing your homework for you. Conservation of energy and momentum are good places to start, do you know why?
Well since it's an elastic collision I know Kf=Ki and due to the conservation of momentum Pf=Pi but i don't know how to put these two equations together to determine which height each of the blocks rises too. I can't really understand how the book uses the equations since the explanation is very vague. I guess I'm more confused since they don't give number values in this problem.
 

Related to Elastic Collision of Blocks on a Half-Pipe: How to Determine the Final Heights?

1. What is an elastic collision?

An elastic collision is a type of collision between two objects in which both kinetic energy and momentum are conserved. This means that the total energy and momentum of the system before and after the collision remains the same.

2. How is an elastic collision different from an inelastic collision?

In an elastic collision, both kinetic energy and momentum are conserved, while in an inelastic collision only momentum is conserved. In an inelastic collision, some of the kinetic energy is lost and converted into other forms of energy, such as heat or sound.

3. What is the equation for calculating the final velocities in an elastic collision?

The equation for calculating the final velocities in an elastic collision is v1 = [(m1 - m2) * v1i + 2m2 * v2i] / (m1 + m2) and v2 = [(m2 - m1) * v2i + 2m1 * v1i] / (m1 + m2), where v1 and v2 are the final velocities of the two objects, m1 and m2 are their masses, and v1i and v2i are their initial velocities.

4. Is there an example of a real-world elastic collision?

Yes, an example of a real-world elastic collision is when two billiard balls collide on a pool table. In this case, both the kinetic energy and momentum of the system are conserved, with the balls bouncing off each other with the same speed and direction as before the collision.

5. What are the assumptions made in an elastic collision problem?

The assumptions made in an elastic collision problem include: 1) the objects involved in the collision are rigid and do not deform, 2) there is no external force acting on the system, 3) the collision is instantaneous, and 4) there is no loss of energy due to friction or other factors.

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