Question

A railroad freight car, mass 15 000 kg, is allowed to coast along a level track at a speed of 2.0 m/s. It collides and couples with a 50 000-kg loaded second car, initially at rest and with brakes released. What percentage of the initial kinetic energy of the 15 000-kg car is preserved in the two-coupled cars after collision

Answer 1

23.0760769 %

Step-by-step explanation:

`m_1` = Mass of freight car = 15000 kg

`m_2` = Mass of second car = 50000 kg

`v_1` = Velocity of freight car = 2 m/s

`v_2` = Velocity of second car = 0

v = Combined mass velocity

As the linear momentum of the system is conserved we have

`m_1v_1+m_2v_2=(m_1+m_2)v\\\Rightarrow v=(m_1v_1+m_2v_2)/(m_1+m_2)\\\Rightarrow v=(15000* 2+50000* 0)/(15000+50000)\\\Rightarrow v=0.46153\ m/s`

The initial kinetic energy

`K_i=(1)/(2)15000* 2^2\\\Rightarrow K_i=30000\ J`

Final kinetic energy

`K_f=(1)/(2)(15000+50000)* 0.46153^2\\\Rightarrow K_f=6922.82307\ J`

The percentage is given by

`(6922.82307)/(30000)* 100=23.0760769\ \%`

The change in percentage of initial kinetic energy is 23.0760769 %