Question

An empty freight car with a mass of 10,000 kg rolls at 5 m/s along a level track and collides with a loaded car

with a mass of 20,000 kg, standing at rest with breaks released. Friction can be neglected. If the cars couple

together, find their velocities after the collision.

b) Find the decrease in kinetic energy as a result of the collision.

c) With that speed should the loaded car be rolling toward the empty car for both to be brought to rest

collision?

Answer 1

Given:

$m=10000\:\rm kg$

$M=20000\:\rm kg$

$v=5\:\rm m/s$

(a)

$$mv=(m+M)u$$

$$u=\frac{mv}{m+M}=\frac{10000*5}{10000+20000}=1.67\:\rm m/s$$

(b)

$$\Delta E=\frac{mv^2}{2}-\frac{(m+M)u^2}{2}$$

$$\Delta E=\frac{10000*5^2}{2}-\frac{(10000+20000)*1.67^2}{2}$$

$$=8.33*10^4\:\rm J$$

(c)

$$mv=MV$$

$$V=\frac{mv}{M}=\frac{10000*5}{20000}=2.5\:\rm m/s$$