How Do You Calculate Velocity and Energy in an Elastic Collision?

In summary, the problem involves two blocks, A and B, moving on a frictionless surface towards each other with block A initially moving with a velocity of 9.00 m/s. The collision is head-on and the blocks have ideal spring bumpers. The maximum energy stored in the spring bumpers and the velocities of the blocks at the time of the collision are to be found. Using the equations for kinetic energy and net work, the elastic potential energy is determined by subtracting the kinetic energies before and after the collision. The velocities of the blocks are found by setting their final velocities equal to each other and using conservation of momentum. The maximum energy stored in the spring bumpers is found to be 105 J, and the velocities of
  • #1
irun4edmund
14
0

Homework Statement


Blocks A (mass 3.50 kg) and B (mass 10.00 kg) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 9.00 m/s. The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of A.

Find the maximum energy stored in the spring bumpers and the velocity of each block at the time of the collision.


Homework Equations


K = 0.5mv2
Wnet = Kf - Ki

The Attempt at a Solution


Since the block A is the only block in motion wouldn't the elastic potential energy be equal to the kinetic energy? I tired using 0.5m(v)^2 and setting that equal to the Kinetic energy, but i didn't get the right answer (i got 141.75).

As far as solving for the velocity of blocks A and B, I'm not sure how to go about it. i tried using Vaf = [(3.5-10.0) / 13.5] * 9.00 = 4.3 but this is the velocity of block A right after the collision not during (answer to another part of the question, but it doesn't help me with the first part).

Any help on this would be greatly appreciated. thanks guys.
 
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  • #2
Welcome to PF!

irun4edmund said:
Find the maximum energy stored in the spring bumpers and the velocity of each block at the time of the collision.
…
Since the block A is the only block in motion wouldn't the elastic potential energy be equal to the kinetic energy?

Hi irun4edmund! Welcome to PF! :smile:

No, elastic PE = KE before minus KE after.

Hint for velocities: when the spring is at maximum compression, what is the relative velocity of the blocks?
 
  • #3
ok i tried PE = 0.5mavai2 -0.5mavaf2-0.5mbvbf2 and got 3.55 J. That wasn't right either...

If the compression of the springs was at an maximum, wouldn't the relative velocities be zero? that was my intial guess and that wasn't right either.
 
Last edited:
  • #4
irun4edmund said:
If the compression of the springs was at an maximum, wouldn't the relative velocities be zero? that was my intial guess and that wasn't right either.

Hi irun4edmund! :smile:

That is correct … then you combine vaf = vbf with conservation of momentum to find what they are. :smile:
 
  • #5
Oh.. my.. god. It worked. I never would have thought to set Va = Vb I though i was working 2 equations with 3 unknowns.

I got Va = Vb = 2.33 m/s

Elastic Potential = 105 J

Thank you!
 

Related to How Do You Calculate Velocity and Energy in an Elastic Collision?

1. What is an elastic collision?

An elastic collision is a type of collision between two objects where both the total kinetic energy and momentum are conserved. This means that after the collision, the total energy and momentum of the objects remain the same as they were before the collision.

2. What are the conditions for an elastic collision to occur?

The conditions for an elastic collision to occur include: the objects must be moving in a straight line, there must be no external forces acting on the objects, and the objects must be made of materials that do not deform or lose energy during the collision.

3. How is the coefficient of restitution related to elastic collisions?

The coefficient of restitution is a measure of how elastic a collision is. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach. In elastic collisions, the coefficient of restitution is equal to 1, indicating a perfectly elastic collision.

4. Can any type of collision be considered elastic?

No, only certain collisions can be considered elastic. Inelastic collisions, where some energy is lost during the collision, are much more common in real-world scenarios. Perfectly elastic collisions are rare and typically only occur at the atomic level.

5. How is the conservation of momentum used to solve elastic collision problems?

The conservation of momentum is an important principle used in solving elastic collision problems. It states that the total momentum of a system remains constant before and after a collision. By setting up equations using this principle, we can solve for unknown variables such as the velocities of the objects before and after the collision.

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