Elastic Collision: Max Potential Energy Stored

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Homework Help Overview

The problem involves an elastic collision between a 2kg block and a 3kg block fitted with a spring. The original poster seeks to determine the maximum elastic potential energy stored in the spring during the collision, given the initial conditions and options for potential energy values.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the conservation of momentum and kinetic energy as methods to find the velocities of the blocks post-collision. Some express uncertainty about the relationship between the blocks' velocities and the spring's compression. Others mention using equations and models to explore the problem further.

Discussion Status

The discussion includes various interpretations of the problem, with some participants suggesting that the velocities of the blocks must be equal at maximum compression. There is acknowledgment of different approaches, including the use of equations and spreadsheet modeling, although no consensus on a definitive solution has been reached.

Contextual Notes

Participants note the challenge of the problem, with some expressing confusion about the calculations and the implications of the spring constant not being provided. There is also mention of differing results from calculations, indicating potential issues with assumptions or methods used.

karis
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Homework Statement


The figure shows a 2kg block moving at a speed of 0.5ms-1 on a smooth horizontal surface. It collides head-on elastically with an initially stationary block of mass 3kg which is fitted with a light spring. What is the maximum elastic potential energy stored in the spring during collision?
A. 0.10J
B. 0.15J
C. 0.25J
D. It cannot be found as the force constant of the spring is not known.

Homework Equations





The Attempt at a Solution


if i treated the collision as an elastic one, i can't get the velocity of the two blocks, (i used the method of conservation of momentum)

Thank you! =)
 

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This is a very interesting and difficult question!
I don't know how to do it.
If you use KE before = KE after, you get a second equation and can solve the pair of them for the the velocities of both carts after the collision. But this doesn't seem to help.

As the first cart contacts the spring on the second, there will be a force on both carts. The spring will compress and the force will increase (F = kx) until . . . . .
Answer that question and we'll have a grip on the problem!
 
I've been working on this for quite a while. I actually found a way to solve it using a system of 3 equations and then getting the maximum on a quadratic equation for the compression of the spring. I didn't get one of the choices given in the question. I also did it with a spreadsheet model and got the same answer. Kind of interesting! I would sure like to hear what the correct solution is.
 
This isn't a difficult problem. Two things are conserved: momentum and energy. At the moment of maximum compression, the two blocks have to be moving at the same speed; if they weren't, the spring would either stretch or continue to compress. With the conservation of momentum equation you can get this speed; with this speed you can calculate how much energy must be stored away in the spring.
 
thanks so much!=]
i keep on calculating their velocities coz i thought they're different
but i got it now!

btw, the correct answer is 0.15J
 
Thanks, ideas! I actually figured that out in the middle of the night - and found the error in my spreadsheet this morning.
 

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