Question

A car of mass m1 stopped at a traffic light is rear-ended by a car with mass m2. The cars become entangled. The second car was moving at a velocity of v2 before the collision. What is the kinetic energy of the system after the collision?

Answer 1

By momentum conservation we can find the final velocity of two cars

`m_1v_(1i) + m_2v_(2i) = m_1v_(1f) + m_2v_(2f)`

now we know that they combined together after collision and first car is at rest initially

`m_2v_2 = (m_1 + m_2)v`

`v = (m_2v_2)/(m_1 + m_2)`

now the kinetic energy of two combined cars is

`KE = (1)/(2)(m_1 + m_2)((m_2v_2)/(m_1+m_2))^2`

`KE = (1)/(2)((m_2^2v_2^2)/(m_1 + m_2))`