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

Answer:

23.0760769 %

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

$m_1v_1+m_2v_2=(m_1+m_2)v\\\Rightarrow v=\dfrac{m_1v_1+m_2v_2}{m_1+m_2}\\\Rightarrow v=\dfrac{15000\times 2+50000\times 0}{15000+50000}\\\Rightarrow v=0.46153\ m/s$

The initial kinetic energy

$K_i=\dfrac{1}{2}15000\times 2^2\\\Rightarrow K_i=30000\ J$

Final kinetic energy

$K_f=\dfrac{1}{2}(15000+50000)\times 0.46153^2\\\Rightarrow K_f=6922.82307\ J$

The percentage is given by

$\dfrac{6922.82307}{30000}\times 100=23.0760769\ \%$

The change in percentage of initial kinetic energy is 23.0760769 %