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1. A 4,500 kg railway train moves east at a velocity of 5 m/s on a level frictionless track when it collides with a stationary 6,500 kg coach train. If the two trains lock together upon impact, how fast do they move after collision?2. A 945 kg car moves to the right at a velocity of 18 m/s collides with a stationary truck of unknown mass. The two vehicles stick together and move off at a velocity of 7 m/s. What is the mass of the truck

Question

  1. A 4,500 kg railway train moves east at a velocity of 5 m/s on a level frictionless track when it collides with a stationary 6,500 kg coach train. If the two trains lock together upon impact, how fast do they move after collision?2. A 945 kg car moves to the right at a velocity of 18 m/s collides with a stationary truck of unknown mass. The two vehicles stick together and move off at a velocity of 7 m/s. What is the mass of the truck
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Solution

  1. To solve this problem, we will use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Before the collision, the momentum of the railway train is (mass x velocity) = 4500 kg * 5 m/s = 22500 kg*m/s. The coach train is stationary, so its momentum is 0.

After the collision, the two trains are locked together, so their total mass is 4500 kg + 6500 kg = 11000 kg. Let's denote their common velocity as V.

So, we have:

22500 kg*m/s (momentum before) = 11000 kg * V (momentum after)

Solving for V gives V = 22500 kg*m/s / 11000 kg = 2.045 m/s. So, the two trains move at a velocity of 2.045 m/s after the collision.

  1. Similarly, we use the principle of conservation of momentum. Before the collision, the momentum of the car is 945 kg * 18 m/s = 17010 kg*m/s. The truck is stationary, so its momentum is 0.

After the collision, the two vehicles move together at a velocity of 7 m/s. Let's denote the mass of the truck as M.

So, we have:

17010 kg*m/s (momentum before) = (945 kg + M) * 7 m/s (momentum after)

Solving for M gives M = (17010 kg*m/s / 7 m/s) - 945 kg = 1929.29 kg. So, the mass of the truck is approximately 1929.29 kg.

This problem has been solved

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