Question

A loaded coal truck ,of mass 10000kg is travelling at 7.8m/s along a horizontal railway track when it bumps into ,and join on to ,three empty trucks of total mass 3000kg .What is the initial speed of the trucks ? how much energy is lost on impact ?

Answer 1

Use conservation of momentum,
\[\Sigma m _{i}u_{i} = \Sigma m_iv_i\]
ui=velocities before impact, and
vi = velocities after impact.

Loss of energy:
\[\Delta E = (1/2)(\Sigma m_iv_i ^{2} \ - \ \Sigma m_iu_i^2)\]

Answer 2

can show the clear way then Mathmate

Answer 3

\[\Sigma \ m_iu_i = 10000*7.8 = (10000+3000)*v\]
where v is the common velocity.
so
v=10000*7.8/13000=6 m/s

Initial energy = (1/2)10000*7.8^2=304200 j
Final energy = (1/2)13000*6^2 = 234000 j
Can you calculate the energy lost?