Question

An object having mass 850 kg and traveling at speed 0.700c collides with a stationary object having mass 1400 kg. The two objects stick together

a) Find the speed of the composite object.
(b) Find the mass of the composite object.

Answer 1

We know form the formula, m = m_o/(1 -v²/c²)^1/2
Here m_o= rest mass
m_1o= 850 kg, v = 0.700c, so m₁ = 850/(1 -0.700²)^1/2 = 1190 kg
m₂ = m_2o =1400 kg.
Let the mass of the composition object be M, its velocity beV.

From law of conservation of linear momentum,

m₁v = MV
so MV = 1190*0.700c = 833c      (1)

energy conservation:
m₁c² + m₂c² =Mc²
so m₁ + m₂ = M
M = 1190 + 1400 = 2590 kg
plug it into (1) V = 833c/2590 = 0.32c
the rest mass of the composition object is
M_o = M(1 - V²/c²)^1/2 =2590(1 - 0.32²)^1/2 = 2453kg