Chapter 09, Problem 048 Partide A and pirt de a are held together with a compres

Question

Chapter 09, Problem 048 Partide A and pirt de a are held together with a compressed spring between them when they are released, the spring pushes them apart and they then fly off in opposite directions, free of the spring. The mass of A is 5.00 times the mass of B, and the energy stored in the spring was 55 J. Assume that the spring has negligible mass and that all its stored energy is transferred to the particles. Once that transfer is complete, what are the kinetic energies of (a) particle A and (b) particle B? Unit (a) Number (b) Number Unit

Explanation / Answer

Final momentum = = the initial momentum
m1v1+m2v2= 0
5m2 v1 +m2v2= 0 since m1 = 5m2
5v1 +v2= 0
v2 = -5v1------------------1
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Kinetic energy of A = E1 = 0.5m1v1^2
Kinetic energy of B = E2 = 0.5m2v2 ^2
= (25/5) 0.5m1v1^2 = 5E1.since m2 = m1/5 and v2 =-5v1
--------------------------------------...
0.5kx^2 = E1 + E2 = 6E1
55 = 6E1
E1 = 9.2 J
E2 = 5E1 = 46 J
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Kinetic energy of particle A is 9.2 J
Kinetic energy of particle B is 5*9.2 = 46 J
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