A satellite,initially at rest in deep space,separates into two pieces,which move away from each other.One piece has a rest mass of 190 kg and moves away with a speed 0.280c,and the second piece moves in the opposite direction with a speed 0.600c.What is the rest mass of the second piece?
A)88.7 kg
B)79.6 kg
C)73.9 kg
D)68.8 kg
E)52.7 kg

Question

Quizplus · Accepted Answer

We can use conservation of momentum and conservation of energy to solve this problem.
Let the initial mass of the satellite be M, and the rest mass of the second piece be m.

Conservation of momentum:
p1 + p2 = 0
where p1 is the momentum of the first piece and p2 is the momentum of the second piece.

p1 = mv1/sqrt(1 - v1^2/c^2) (using relativistic momentum)
p2 = mv2/sqrt(1 - v2^2/c^2)
where v1 = 0.280c and v2 = -0.600c (opposite direction)

Thus, mv1/sqrt(1 - v1^2/c^2) - mv2/sqrt(1 - v2^2/c^2) = 0

Solving for m, we get:
m = M(sqrt(1 - v2^2/c^2)/(v2/c - v1/c))

Using the given values, we get:
m = 73.9 kg (approximately)

Therefore, the rest mass of the second piece is 73.9 kg.

A Satellite,initially at Rest in Deep Space,separates into Two Pieces,which