Find the mass, in metic tons, of the second car.

Question

A train car with mass 37.0 metric tons rolls on a track with a speed of v₁ = 3.72 m/s. It collides and couples with a stationary car. After the collision, the two cars rolls together with a speed of v₂ = 1.51 m/s. Find the mass, in metic tons, of the second car.

Answer 1

We can use the principle of the conservation of momentum - the initial total momentum equals

the final total momentum.

The initial total momentum P_i is the sum of the initial momenta of the 2 blocks:

P_i = m₁*v₁ + m₂*v₂

... where the m's are the masses of the blocks, and the v's are the initial velocities of the blocks

Because the initial velocity v₂ of block 2 is 0, when can simplify that equation to be:

P_i = m₁*v₁

The final total momentum P_f is the sum of the final momenta of the 2 blocks:

P_f = m₁*v_1f + m₂*v_2f

... where v_1f and v_2f are the final velocities of the 2 blocks

Since the 2 blocks have the same final velocity v_f as each other:

P_f = m₁*v_f + m₂*v_f

Equating the initial and final momenta:

m₁*v₁ = m₁*v_f + m₂*v_f

From that equation we can solve for m₂ - the mass, in metric tons, of the second car:

m₂ = (m₁*v₁ - m₁*v_f)/v_f

Using the given values:

m₁ = 37.0 metric tons

v₁ = 3.72 m/s

v_f = 1.51 m/s

... we can solve for the mass of block 2:

m₂ = (37.0*3.72 - 37.0*1.51)/1.51 = 54.15 metric tons