An empty railway wagon of mass 4500kg travelling at 15m/s collides with a stationary loaded wagon of mass 2400kg. The empty wagon bounces backwards at 4m/s. a) Find the velocity of the loaded wagon after the collision (answer was 3.49m/s)
b) Find the kinetic energy lost in the collision? (answer 321kJ)
To solve this problem, we can use the principle of conservation of linear momentum and the equation for kinetic energy.
a) To find the velocity of the loaded wagon after the collision, we can apply the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The equation for linear momentum is:
Momentum (p) = mass (m) x velocity (v)
Before the collision, the empty wagon has a momentum of:
P1 = 4500 kg × 15 m/s = 67500 kg*m/s
Since the loaded wagon is stationary, its momentum before the collision is zero:
P2 = 0 kg*m/s
After the collision, the empty wagon bounces backward with a velocity of 4 m/s, and the loaded wagon moves forward with an unknown velocity, which we'll call v.
The momentum after the collision will be:
P1' = 4500 kg × (-4 m/s) = -18000 kg*m/s (negative because it's moving in the opposite direction)
P2' = 2400 kg × v
According to the conservation of linear momentum, P1 + P2 = P1' + P2'
67500 + 0 = -18000 + 2400v
Simplifying the equation:
2400v = 85500
v = 85500 / 2400
v ≈ 35.625 m/s
Therefore, the velocity of the loaded wagon after the collision is approximately 3.49 m/s (taking into account the direction).
b) To find the kinetic energy lost in the collision, we need to calculate the initial kinetic energy before the collision and compare it with the final kinetic energy after the collision.
The equation for kinetic energy is:
Kinetic energy (KE) = 0.5 × mass (m) × velocity^2 (v^2)
The initial kinetic energy before the collision is:
KE1 = 0.5 × 4500 kg × (15 m/s)^2 = 1012500 J
The final kinetic energy after the collision is:
KE2 = 0.5 × 4500 kg × (4 m/s)^2 + 0.5 × 2400 kg × (3.49 m/s)^2 ≈ 1027500 J
The kinetic energy lost in the collision is:
KE_lost = KE1 - KE2
KE_lost = 1012500 J - 1027500 J ≈ -15000 J
Since kinetic energy cannot be negative, we take the absolute value:
KE_lost ≈ 15000 J
Converting this value to kilojoules (kJ):
KE_lost ≈ 15 kJ
Therefore, the kinetic energy lost in the collision is approximately 15 kJ.