Particle A and particle B are held together with a compressed spring between the
ID: 1617116 • Letter: P
Question
Particle A and particle B 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 8.00 times the mass of B, and the energy stored in the spring was 71 J. Assume that the spring has negligible mass and that all its stored energy is transferred to the particles.
(a) Once that transfer is complete, what is the kinetic energy of particle A?
J
(b) Once that transfer is complete, what is the kinetic energy of particle B?
j
Explanation / Answer
a) b) After the release, let v1 and v2 be the velocity of the two particles A and B.
From the conservation of momentum, we have
Final momentum of particles= Initial momentum of particles
m1v1 + m2v2= 0
8m2 v1 + m2v2= 0 since m1 = 8m2 (given)
8v1 + v2= 0
v2 = -8v1
Kinetic energy of A = E1 = 0.5 m1 (v1)^2
Kinetic energy of B = E2 = 0.5 m2 (v2 )^2
= 0.5 (m1/8)(64 v1^2)
E2 = 4E1 since m2 = m1/8 and v2 = -8v1
From the conservation of energy, we have
0.5kx^2 = E1 + E2 = 5E1
71 =5E1
E1 = 14.2 J
and E2 = 4E1 = 56.8 J
Kinetic energy of particle A is 14.2 J
Kinetic energy of particle B is = 56.8 J ANS