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

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SUMMARY

The discussion focuses on calculating the maximum energy stored in spring bumpers and the velocities of two blocks during an elastic collision. Block A, with a mass of 3.50 kg, moves at 9.00 m/s towards block B, which has a mass of 10.00 kg and is initially at rest. The maximum elastic potential energy was determined to be 105 J, while the velocities of both blocks after the collision were calculated to be 2.33 m/s. Key equations used include kinetic energy (K = 0.5mv²) and the principle of conservation of momentum.

PREREQUISITES
  • Understanding of kinetic energy calculations (K = 0.5mv²)
  • Knowledge of conservation of momentum principles
  • Familiarity with elastic collisions and elastic potential energy concepts
  • Basic algebra for solving equations involving multiple variables
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  • Study the principles of conservation of momentum in elastic collisions
  • Learn how to derive elastic potential energy from kinetic energy changes
  • Explore the concept of relative velocity in elastic collisions
  • Practice problems involving multiple objects in elastic collisions
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irun4edmund
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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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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?
 
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:
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:
 
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!
 

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