Finding the value of the coefficient of elasticity for a 1D collision.

[Lemansky]

Hi all first post. Myself and my friends are very much stumped by this question. Any help would be much appreciated!

Homework Statement

A body with mass m collides directly with a body of mass 3m. If two thirds of the original kinetic energy is lost, find the coefficient of elasticity for this collision.

Homework Equations

Conservation of momentum: m1u1+ m2u2=m1v1+m2v2.

Newton's empirical law: v2-v1= -e(u2-u1)

Loss in kinetic energy: (1/2)m1(u1)^2+(1/2)m2(u2)^2=(1/2)m1(v1)^2+(1/2)m2)v2)^2.

The Attempt at a Solution

Using all the info given and giving the sphere of mass m initial velocity u and final velocity v1, and the sphere of mass 3m initial velocity of 0 and a final velocity of v2 we derived three equations, as follows,

1) u=v1+3v2 from the conservation of momentum.

2)u^2=3(v1)^2+9(v2)^2 from the fact that the final kinetic energy equals a third of the initial kinetic energy,

3)(v2-v1)/e =u from rearranging Newton's empirical law.


By squaring out equation 1 and setting it equal to equation 2 we found that v1=3v2.

No matter which way we approached the problem the same equations always fell out and by juggling them around we were able to get values for e with one problem, they were always negative (but had they been positive they would have been realistic). We are probably making some simple mistake with signs or we're cancelling out somehting which can't be canceled but we really are stuck.


Any help much appreciated!

 

[member 553083]

From the equations you derived, you can solve for the coefficient of elasticity. From equation 1, you have v1 = u-3v2, and from equation 3, you have u = (v2-v1)/e. Substituting the expression for v1 into equation 3 and rearranging, you get e = (v2-u+3v2)/u = (4v2-u)/u. Using the expression for u from equation 2, you can substitute it into the equation for e and solve for v2. Then, substitute the expression for v2 into the equation for e to get your answer.