a locomotive of mass 15000kg traveling at 2.5m/s collides and couples with a set of rail carts of mass 7000kg.calculate:
1.the combined velocity of the train and carts after impact
2.the loss in kinetic energy in the collision
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Now this time you told me the collision is inelastic, they stick together.
Therefore we have one mass of 22,000 kg after collision.
I assume the carts were stationary before the crash.
Initial momentum=
15,000*2.5 + 0 = 37,500 kg m/s
= final momentum = 22,000 v
so
v = 1.68 m/s
initial Ke = (1/2) (15,000)(2.5)^2
final Ke = (1/2)(22,000)(1.68)^2
subtract the final from the initial to find the loss in the heat of collision
To calculate the combined velocity of the train and carts after impact, we can use the principle of conservation of momentum. In an isolated system, the total momentum before the collision is equal to the total momentum after the collision.
1. Calculating the combined velocity:
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v).
The total initial momentum before the collision is: p_initial = m_train * v_train + m_carts * v_carts
Let's substitute the values given:
m_train = 15,000 kg (mass of the locomotive)
v_train = 2.5 m/s (velocity of the locomotive)
m_carts = 7,000 kg (mass of the carts)
v_carts = 0 m/s (initial velocity of the carts since they were stationary before the impact)
Initial momentum (p_initial) = 15,000 kg * 2.5 m/s + 7,000 kg * 0 m/s
= 37,500 kg·m/s
To find the combined velocity, divide the total initial momentum by the combined mass of the train and carts:
Combined mass = m_train + m_carts
Combined mass = 15,000 kg + 7,000 kg
= 22,000 kg
Combined velocity (v_combined) = p_initial / Combined mass
= 37,500 kg·m/s / 22,000 kg
≈ 1.70 m/s
Therefore, the combined velocity of the train and carts after impact is approximately 1.70 m/s.
2. Calculating the loss in kinetic energy:
The loss in kinetic energy in the collision can be determined by calculating the initial kinetic energy and the final kinetic energy, then finding their difference.
Initial kinetic energy (KE_initial) = 0.5 * m_train * (v_train)^2 + 0.5 * m_carts * (v_carts)^2
Let's substitute the values given:
m_train = 15,000 kg (mass of the locomotive)
v_train = 2.5 m/s (velocity of the locomotive)
m_carts = 7,000 kg (mass of the carts)
v_carts = 0 m/s (initial velocity of the carts since they were stationary before the impact)
KE_initial = 0.5 * 15,000 kg * (2.5 m/s)^2 + 0.5 * 7,000 kg * (0 m/s)^2
= 93,750 J + 0 J
= 93,750 J
Final kinetic energy (KE_final) = 0.5 * (m_train + m_carts) * (v_combined)^2
Using the values obtained earlier:
Combined mass = 22,000 kg (combined mass of the train and carts)
v_combined = 1.70 m/s (combined velocity after impact)
KE_final = 0.5 * 22,000 kg * (1.70 m/s)^2
≈ 33,860 J
The loss in kinetic energy (ΔKE) = KE_initial - KE_final
= 93,750 J - 33,860 J
≈ 59,890 J
Therefore, the loss in kinetic energy in the collision is approximately 59,890 Joules.