Momentum and Energy: Find Maximum Energy Stored in Bumper

[zhuyilun]

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 2.00 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 positive x be the direction of the initial motion of a.

find maximum energy stored in the bumper and the velocity of a and b at that time

Homework Equations

The Attempt at a Solution

this question seems easy, but i just don't know how to start. can anyone give me a hint?

 

[cepheid]

Conservation of energy is a good place to start. You know how much kinetic energy block a initially has. Therefore, you know how much energy is going to be stored in the springs as elastic potential energy.

 

[zhuyilun]

Conservation of energy is a good place to start. You know how much kinetic energy block a initially has. Therefore, you know how much energy is going to be stored in the springs as elastic potential energy.

initially a has 0.5*(2)^2*3.5=7 j energy. i tried, but this is not the correct answer

 

[Relay]

You need to set up two equations and two unknowns. In this case your momentum and KE both give you the same numeric value. Set up one equation for momentum after collision. Set up you second equation for the KE after collision. Then solve for the velocity of the smaller mass using the two equations and two unkown velocities. When you solve for the smaller mass velocity you will get two roots. One will be the initial velocity and is the situation when the second mass doesn't move. Use the other value to solve for the velocity of the heavier mass. Good Luck.