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