Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 160,000 kg and a velocity of 0.300 m/s, and the second having a mass of 115,000 kg and a velocity of -0.120 m/s. (The minus indicates direction of motion.) What is their final velocity?
Physics questions
Well, if we're talking about train cars, I hope this isn't a "loco" question. Now, let's do some math and try not to derail our train of thought.
To find the final velocity, we need to use the principle of conservation of momentum. The total momentum before the collision should be equal to the total momentum after the collision. (By the way, I hope these train cars have good insurance for their "bump"!)
The formula for momentum is given by: momentum = mass x velocity.
For the first train car: momentum1 = (mass1)(velocity1) = (160,000 kg)(0.300 m/s).
For the second train car: momentum2 = (mass2)(velocity2) = (115,000 kg)(-0.120 m/s).
Now, since momentum is conserved, we can add the two momenta together to get the total momentum after the collision:
Total momentum = (momentum1) + (momentum2).
After plugging in the numbers, we can calculate the total momentum and then find the final velocity by dividing that total momentum by the combined mass of the two train cars.
To calculate the final velocity of the train cars after they collide, we can use the concept of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v). Mathematically, it is represented as p = m * v.
In this case, we have two train cars moving toward each other with given masses and velocities. Let's label the first train car as Train A and the second train car as Train B.
The momentum before the collision is the sum of the momentum of Train A and Train B:
Initial momentum = (mass of Train A * velocity of Train A) + (mass of Train B * velocity of Train B)
= (160,000 kg * 0.300 m/s) + (115,000 kg * -0.120 m/s)
Now, we can calculate the initial momentum and then apply the principle of conservation of momentum to find the final velocity.
Initial momentum = (160,000 kg * 0.300 m/s) + (115,000 kg * -0.120 m/s)
= 48,000 kg·m/s - 13,800 kg·m/s
= 34,200 kg·m/s
Since momentum is conserved, the total momentum after the collision will also be 34,200 kg·m/s.
Now, to find the final velocity, we need to consider that the two train cars will stick together after the collision. Since they are moving in opposite directions, the final velocity will be negative.
Final momentum = Total mass * Final velocity
Given that the total mass is the sum of the mass of Train A and Train B:
Total mass = mass of Train A + mass of Train B
= 160,000 kg + 115,000 kg
= 275,000 kg
Now we can rearrange the formula to solve for the final velocity:
Final velocity = Final momentum / total mass
= 34,200 kg·m/s / 275,000 kg
= 0.1244 m/s (approx)
Therefore, the final velocity of the two train cars after colliding will be approximately -0.1244 m/s.
Conservation of Linear Momentum:
M1V1 + M2V2 = M1*V3 + M2*V3
M1 = 160,000 kg
V1 = 0.30 m/s
M2 = 115,000 kg
V2 = -0.120 m/s
Solve for V3, the final velocity.