Solving Momentum Problem: Superman & Metropolis Express Collision

[runningirl]

Homework Statement

Lois Lane has been tied to the tracks and the Metropolis Express (m=200, 000 kg) is racing toward her at a velocity of +30 m/s. Superman (m=100kg) arrives just in time and comes hurtling at the train, collides with it, and stops it just before it runs over Lois. NOTE: Both Superman and the train come to a stop.

a)What was Man of Steel's velocity prior to his collision with the train?

b) It took 0.20 seconds for the train, and Superman, to come to a stop, what was the average force exerted by Superman on the train?

c) What was the average force exerted by the train on Superman?

Homework Equations

The Attempt at a Solution

i thought for part a:

200000(0)+100(v)=200000(30)+100(0)

v=6000 m/s?! it doesn't make sense..

part b)

J=Fave(t)
P=m(V)

100(v)=Fave(.2)

I realized i had to find Superman's velocity...

 

[cdotter]

Check your calculation, your answer is smaller than what it should be (by a factor of ten.)

But even with your smaller answer, why doesn't it make sense? A 200,000 kg train moving at 30 m/s has a lot of momentum.

 

[runningirl]

Check your calculation, your answer is smaller than what it should be (by a factor of ten.)

But even with your smaller answer, why doesn't it make sense? A 200,000 kg train moving at 30 m/s has a lot of momentum.

sorry, it was 60,000!
what does it mean for the average force exerted by the train on superman?!

 

[runningirl]

also, i got 60, 000, 000 N for part b...
which doesn't seem right for superman who has a mass of 100 kg..
Favg(.2)=100(60,000)

 

[rwisz]

Okay, let's break this down step by step. First, let's start with part a. The equation you used, m1v1 + m2v2 = m1v1' + m2v2', is a valid equation to use in this problem. However, you need to be careful with your signs. In this case, the positive direction is defined as the direction of motion of the train, so the initial velocity of the train is +30 m/s and the final velocity is 0 m/s. The initial velocity of Superman is unknown, so we can use v as a variable. The final velocity of Superman is 0 m/s, since he comes to a stop. So, our equation becomes:

200000(30) + 100(v) = 200000(0) + 100(0)

Now, let's solve for v:

200000(30) + 100(v) = 0

6000000 + 100v = 0

100v = -6000000

v = -60000 m/s

This negative velocity makes sense, since Superman is moving in the opposite direction of the train.

Now, let's move on to part b. The equation you used, J = Fave(t), is also a valid equation to use. However, we need to be careful with our units. Joules (J) is a unit of energy, not force. The correct equation to use in this case is:

Fave = mΔv / Δt

Where m is the mass of the train (200000 kg), Δv is the change in velocity (30 m/s), and Δt is the time it takes for the train to come to a stop (0.2 seconds). Plugging in these values, we get:

Fave = (200000 kg)(30 m/s) / (0.2 s)

Fave = 3000000 N

So, the average force exerted by Superman on the train is 3,000,000 Newtons.

Finally, for part c, we can use the same equation as part b, but with the mass and change in velocity of Superman. So, the average force exerted by the train on Superman is:

Fave = (100 kg)(-60000 m/s) / (0.2 s)

Fave = -3000000 N

This negative sign indicates that the force is in the