Efficiency of a Crane: Calculating Power and Percentage Efficiency

[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.

Homework Equations

p=mv

efficiency=(P_out/P_in)*100%

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=(P_out/P_in)x100%=(24000/250000)x100%=9.6%.

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

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Homework Equations

W+E_p1+E_k1=E_p2+E_k2+H_f

d=v_i+1/2at²

The Attempt at a Solution

First Height(h):

W+E_p1+E_k1=E_p2+E_k2+H_f
E_p1=E_k2
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+E_p1+E_k1=E_p2+E_k2+H_f
E_p1=E_k2
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.

 

[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