Question

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. one is traveling at 0.650c and the other at 0.850c. the satellites collide and stick together. what is the rest mass of the combined object after the collision?

Answer 1

The correct answer is: 200kg

Step-by-step explanation:

Let's apply the law of conservation of momentum:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ -- (1)

u₁ = Initial speed of mass one = -0.650c (negative sign indicates that this is moving towards the second mass)

u₂ = Initial speed of mass two = 0.85c

After collision the two are stick with each other, so according to (1) v₁ = v₂ = v (Final velocity):

The final velocity = v = (m₁u₁ + m₂u₂)/(m₁+m₂) = (-65+85)/(200) = 0.1c (after collision)

Now here is the trick! Most of the students would do the calculation like I did above and use the relativistic mass formula and put the velocity v which we computed above like:

m = m₀(sqrt (1 – v² / c² ))

BUT in the question the REST mass is required! In that case you do not need to apply the above formula; simply add both the mass after collision as they stick together; hence 100 + 100 = 200 kg (rest mass).