Head-on elastic collision between two masses

[mangafan]

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?

 

[physics girl phd]

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.

 

[HallsofIvy]

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?

 

[mangafan]

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

 

[mangafan]

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