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?

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).

Average force = 67 mn

Explanation:

Given:

Initial velocity u = 0 m/s

Final velocity v = 67 m/s

Time t = 1 ms = 0.001 sec.

Computation:

Using Momentum theory

Change in momentum  = F × Δt

 (v-u)/t =  F × Δt

F × 0.001 = (67 - 0)/0.001

F= 67,000,000

Average force = 67 mn