First Year Work and Energy

1. Apr 9, 2012

workandenergy

1. The first problem statement, all variables and given/known data

A crane rated at 2.5x105 W can lift a load of 1.5x104 kg vertically with a speed of 1.6 m/s. Determine the efficiency of the crane. Express your answer as a percentage.

2. Relevant equations

p=mv

efficiency=(Pout/Pin)*100%

3. The attempt at a solution

I first use the momentum equation, P=mv, to solve for the output power. P=15000Jx1.6m/s=24000W. Now, I divide my output power by the input power and times by 100% to get my efficiency. efficiency=(Pout/Pin)x100%=(24000/250000)x100%=9.6%.

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1. The second problem statement, all variables and given/known data

2. Relevant equations

W+Ep1+Ek1=Ep2+Ek2+Hf

d=vi+1/2at2

3. The attempt at a solution

First Height(h):

W+Ep1+Ek1=Ep2+Ek2+Hf
Ep1=Ek2
mgh=1/2mv22
Therefore, v2=√(19.6h)
Assume height is 1 and I get a speed of 4.427188724
v=d/t, therefore my base value of d is 4.427188724

Second Height(2h):

W+Ep1+Ek1=Ep2+Ek2+Hf
Ep1=Ek2
mg2h=1/2mv22
Therefore, v2=√(39.6h)
Assume height is 1 and I get a speed of 6.292853089
v=d/t, therefore my base value of d is 6.292853089

Now I divide both to get the difference and get 1.421410625, which is √2d and thus the answer is B.

2. Apr 10, 2012

ehild

The solution of the second problem is correct.

As for the first problem, P is power, and it is not the same as the momentum p.

Do you know how the power is related to force and velocity?

ehild