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 ?

Question

mathmate · Answer

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:
$$\Delta E = (1/2)(\Sigma m_iv_i ^{2} \ - \ \Sigma m_iu_i^2)$$

anonymous · Answer

can show the clear way then Mathmate

mathmate · Answer

$$\Sigma \ m_iu_i = 10000*7.8 = (10000+3000)*v$$
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?