EK physics 1001 # 375

[2010premed]

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A 10,000 kg locomotive speeds toward Lois Lane at 10 m/s and will hit her in 10s if Superman doesn't try to stop it. If Supermane applies a constant force, what average power does he need in order to stop the train?
A: 2.5 x 10^4

I don't understant how you can know to set up Fd=1/2mv^2 for this one...

 

[lorenzomicron]

power is the work over time, but work is also equal to change in kinetic energy. thus power can be change in kinetic energy over time.

calculate, ki= 1/2mv^2. we need superman to apply a force such that kf=0.

thus, change in k is 1/2 mv^2.

he needs to do this in ten seconds, thus t=10, p=w/10=k/10

p=1/2*m*v^2/10= 5x10^4....unless i put in a wrong number, this is definitely the correct answer.....probably

 

[kehlsh]

above poster is correct, problem 375 has a typo. it is 20 seconds not 10 seconds.. yikes!

 

[lorenzomicron]

then, p=1/2*m*v^2/20= 2.5x10^4

 

[2010premed]

Thanks =)

 

[SoftwareKevin]

An alternative way to solve it is to actually calculate force, then work, then power.

To go from 10m/s over 20 seconds requires a deceleration of 0.5m/s. So
F = m*a = 10000*0.5 = 5000N

Average speed will be 5 m/s (going from 10 m/s to 0 at constant deceleration), so over 20 seconds they will travel 5*20 = 100m.
W = F*d = 5000N*100m = 500000J

Then just calculate power:
P = F / t = 500000 / 20 = 2.5x104

 

[2010premed]

cool, thanks