A railroad car of mass m = 30000 kg moving
at v1 = 2.9 m/s collides and couples with
two coupled railroad cars, each of the same
mass as the single car and moving in the same
direction at v2 = 1.711 m/s.
What is the magnitude of the kinetic energy
lost in the collision?
Answer in units of J
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To find the magnitude of the kinetic energy lost in the collision, you need to calculate the initial kinetic energy before the collision and the final kinetic energy after the collision, and then subtract the final kinetic energy from the initial kinetic energy.
1. Start by calculating the initial kinetic energy before the collision using the formula:
Kinetic Energy = (1/2) * mass * velocity^2
For the single car:
Initial Kinetic Energy1 = (1/2) * m * v1^2
2. Calculate the initial total kinetic energy before the collision for all three cars:
Initial Total Kinetic Energy = 3 * Initial Kinetic Energy1
3. After the collision, the three cars couple together and move with a single velocity. To find this final velocity, you can use the conservation of momentum principle.
Total initial momentum = Total final momentum
(m * v1) + (m * v2) + (m * v2) = (3m) * vf
Where vf is the final velocity.
Solve this equation for vf.
4. Now calculate the final kinetic energy after the collision using the formula (since all three cars are moving with the same velocity):
Final Kinetic Energy = (1/2) * (3m) * vf^2
5. Finally, calculate the magnitude of the kinetic energy lost by subtracting the final kinetic energy from the initial total kinetic energy:
Kinetic Energy Lost = Initial Total Kinetic Energy - Final Kinetic Energy
Plug in the given values (m = 30000 kg, v1 = 2.9 m/s, v2 = 1.711 m/s) into the above equations, solve them step by step, and then subtract to find the magnitude of the lost kinetic energy.