Question

When linking train cars, the 72,500 kg car on the left is moving at a rate of 0.59 m/s while the 90,269 car on the right is moving at a rate of -1.2 m/s. Once linked, how fast will the two train cars be moving?

Answer 1

Using conservation of momentum:

$m1u1+m2u2=m1v1+m2v2$

Where:

m1 = Mass of the car on the left = 72500kg

m2 = Mass of the car on the right = 90269kg

u1 = Initial speed of the car on the left = 0.59 m/s

u2 = Initial speed of the car on the right = -1.2 m/s

v1 = Final speed of the car on the left

v2 = Final speed of the car on the right

Since the train cars will be linked, we can conclude:

v1 = v2

so:

$\begin{gathered} m1u1+m2u2=v1(m1+m2) \\ so\colon \\ v1=\frac{m1u1+m2u2}{m1+m2} \\ v1=\frac{72500\cdot0.59+90269(-1.2)}{72500+90269} \\ v1=-\frac{65547.8}{162769} \\ v1=-0.4\frac{m}{s} \end{gathered}$

Answer:

0.4 m/s