Head-on elastic collision between two masses

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Homework Help Overview

The discussion revolves around a head-on elastic collision involving two masses, where one mass is stationary. The original poster seeks to determine the mass ratio required for the moving mass to lose a quarter of its kinetic energy during the collision.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conditions of elastic collisions and the necessary mathematical relationships. The original poster attempts to apply conservation of momentum and energy principles, while others suggest starting with a mass ratio assumption to simplify the problem. There are questions regarding the setup and the calculations performed.

Discussion Status

The discussion is ongoing, with participants sharing their approaches and equations. Some guidance has been provided regarding the use of conservation laws, but there is no consensus on the correct path forward, as the original poster expresses difficulty in achieving the desired result.

Contextual Notes

There is an emphasis on showing work before receiving assistance, and participants are encouraged to explore related threads for additional context. The original poster has substituted specific values for the masses but has not reached a satisfactory conclusion.

mangafan
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in a head-on elastic collision between two masses, one of which is stationary, a experimenter would like the incident mass to lose quarter of its kinetic energy in the collision. What must be the ratio of the masses of the two objects for this to be the case?
 
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First you need to ask yourself: what are the conditions of elastic collisions? there are some keys that will help you write some mathematical relationships.

Note: You need to show some work to us before we'll help. If you're stuck, you should look at related threads.
 
Good question! What have you done so far?

Since you are only interested in the ratio of masses, you can assume the mass of one is 1 and the other x. Then x is the "ratio of masses" you want. Now, one of them (it doesn't matter which) is stationary (v= 0) and the other has some speed v0. What is the total kinetic energy? Use conservation of energy and conservation of momentum to find the speeds after the collision (which will, of course, depend on both x and v0) so you can find the kinetic energy of each. What should x be so that one that was moving has lost 1/4 of its kinetic energy?
 
I have use the equation v1=(m1-m2)*u1/(m1+m2) and v2=(2m1)*u1/(m1+m2)
then i substitute v1 and v2 into the ke equation. i also substitute m1 = 1 and m2 = x. i did not get the result i want
 
i use two equation v1= (m1-m2)*u1/(m1+m2) and v2= (2m1)*u1/(m1+m2). i substitute m1 = 1 and m2 = x. and then substitute in the ke equation. but i just cannot get the value for x
 

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