EK 1001 Physics Q # 375

[FeatherPen]

Advertisement - Members don't see this ad

I swear this makes no sense...

A 10,000 kg locomotive speeds toward Lois Lane at 10 m/s

It will hit her in 10 s if Superman doesn't try to stop it.

If Superman applies a constant force, what average power does he need in order to stop the train?

Answer: 2.5 x 10^4

Explanation in book:

From v=d/t, we know that the train is 100m from Lois.

From Fd= 1/2mv^2, we know that superman must apply a force of 5,000N to stop the train

From x=1/2at^2 and F=ma, we know that when this force is applied to the train, it will stop in 20 seconds

P = W/t = (1/2mv^2) / t

 

[bobsmith]

So...I think you're asking why it states 10s in the first part of the question, and 20s in the answer?

The 10s is unrelated to the 20s. The 10s is referring to how long it would take for the train to hit Lois Lane, and the 20s is referring to how long the train would take to go 100m if Superman is applying a 5000 N force against the train.

So the steps are as follows:
1) Use the time it takes to hit Lois Lane and the speed at which the train is moving to calculate how far the train is

2) Use this distance as d in Fd = (1/2)mv^2, where m = 10,000kg and v = 10m/s to calculate F = 5000 N.

Now, we have the force that Superman is applying against the train over the distance of 100 meters, bringing the train from its speed of 10m/s to 0m/s.

3) We then use this force and F = ma to calculate the negative acceleration that Superman is exerting on the train. 5,000N/10,000kg = 0.5 m/s^2

Now, we know the distance that this train is traveling (100m) and its deceleration (0.5m/s^2).

4) So now we can calculate how long it takes the train to travel this distance. I'm not sure why they used x=1/2at^2, since (I think) it should be x = (Vo)t + 1/2at^2, which gives you (100 = 10t -1/4t^2 which is 0 = -1/4t^2 + 10t - 100 which is 0 = t^2 - 40t + 400, which gives you t = 20)

but you get t = 20 s either way...so maybe I'm messing something up there.

Anyway, this 20 s is the time it takes for Superman to stop the train, and so you can calculate the work exerted (from 1/2mv^2 above = 500,000J) and divide by 20s to get 2.5x10^4 W.