Respuesta :
Explanation:
The mass of freight car, mâ = 30,000 kg
Velocity of freight car, uâ = 0.85 m/s
Mass of hopper, mâ = 110,000 kg
(a) Let v is the final velocity of the loaded freight car. Initial momentum of the car before the dump, [tex]p_i=30000\ kg\times 0.850\ m/s=25500\ kg-m/s[/tex]
Final momentum, [tex]p_f=(30000\ kg+110000\ kg)v=140000\ v[/tex]
According to the conservation of momentum,
initial momentum = final momentum
25500 kg-m/s = 140000 v
v = 0.182 m/s
So, the  final velocity of the loaded freight car is 0.182 m/s.
(b) Initial kinetic energy, [tex]k_i=\dfrac{1}{2}\times 30000\ kg\times (0.850\ m/s)^2=10837.5\ J[/tex]
Final kinetic energy, [tex]k_f=\dfrac{1}{2}(m_1+m_2)v^2[/tex]
[tex]k_f=\dfrac{1}{2}\times (30000\ kg+110000\ kg)\times (0.182\ m/s)^2=2318.68\ J[/tex]
So, loss in kinetic energy, [tex]\Delta k=k_f-k_i[/tex]
[tex]\Delta k=2318.68\ J-10837.5\ J=-8518.82\ J[/tex]
So, 8518.82 J of kinetic energy is lost after collision. Hence, this is the required solution.
