Question

A truck of mass \[500kg\] moving at \[4m/s\] collides with another truck of mass \[1500kg\] moving in the same direction at \[2m/s\]. What is their common velocity just after the collision if they move off together?

Answer 1

Hint: The impact can be either elastic or inelastic. Elastic collision follows both conservations of momentum and kinetic energy whereas inelastic collision doesn’t obey conservation of kinetic energy. The collision of trucks comes under Inelastic collision wherever kinetic energy is not conserved. Inelastic collision follows Conservation of Momentum. So we can conclude that momentum before the collision is equal to momentum after the collision.

Complete step by step solution:
The term Momentum indicates the quantity that a moving object holds. It is referred to as the product of mass and velocity and its units are $kgm{s^{ - 1}}$or$Ns$. It is denoted by the letter $P$. In this given question, collision of the truck is an inelastic collision that follows conservation of momentum.
Momentum $P = m \times v$,
where \[m\] is the mass of the truck and $v$is the velocity of the truck.
By conservation of momentum,
Momentum before impact = Momentum after impact
Mass of the first truck, \[{m_1} = 500kg\]
Speed of the first truck, \[{u_{1}} = 4m/s\]
Mass of the second truck, \[{m_2} = 1500kg\]
Speed of the second truck, \[{u_2} = 2m/s\]
Combined masses of both the trucks, \[m = 1500 + 500 = 2000kg\]
Combined velocity is taken as \[v\]
According to the law of conservation of momentum, we can say that
\[{m_1}{u_{1}} + {m_2}{u_{2}} = mv\]
\[ \Rightarrow 500 \times 4 + 1500 \times 2 = 2000 \times v\]
\[v = \dfrac{{2000 + 3000}}{{2000}} = 2.5m/s\]

Note:
Once two bodies of equal masses undergo one-dimensional elastic collision, their velocities will get interchanged. Similarly, when an elastic body hits against another body of the same mass, primarily at rest, after the impact the first body comes to rest whereas the second body passes with the initial velocity of the first. When a light body strikes against a heavy body at rest, the light body bounces back after the collision with equal and opposite velocity while the heavy body remains at rest.