Question

Consider two railway trucks that can travel along a straight railway track which defines the

x-axis. A laden truck of mass M = 6.6 × 103 kg and an empty truck of unknown mass m

approach each other at constant velocity. The laden truck has an initial velocity component

of ux = +2.0ms−1 which is half that of the initial velocity component of the empty truck

(but in the opposite direction). After an elastic collision, the velocity component of the laden

truck is halved, but it continues in the same direction. The unknown post-collision velocity

component of the empty truck is vx.

(a) Begin by clearly setting out the masses and velocities of the two trucks, being sure to

express each of the known velocity components in terms of ux. Then write down equations

for the conservation of linear momentum and the conservation of kinetic energy, in terms of

the variables M,m, ux and vx only.

(b) Rearrange the momentum equation into the form: vx = . . . , and rearrange the energy

equation into the form m = . . . . Then combine these simultaneous equations to determine

values, first for m and then for vx, using the known values of M and ux. (Hint : a useful first

step is to find a value for the ratio M/m.)

(c) Use your result for vx to confirm that the relative velocity of approach of the two trucks is

the negative of their relative velocity of separation, as expected for an elastic collision.

Answer 1