Finding tension in a ski boat tow rope from power difference

[Parzival]

Homework Statement

The motor of a ski boat generates an average power of 7.50 * 10^4 W when the boat is moving at a constant speed of 12 m/s. When the boat is pulling the skier at the same speed, the engine must generate an average power of 8.30 * 10^4 W. What is the tension in the tow rope that is pulling on the skier?

Homework Equations

Average power = force * average speed
Average power = change in energy/time
Average power = Work/time

The Attempt at a Solution

I tried setting up an equation:

8.30 * 10^4 W = F*12 m/s
F = 83,000/12 N

= 7 * 10^3 N which is wrong.

 

[ehild]

I tried setting up an equation:

8.30 * 10^4 W = F*12 m/s
F = 83,000/12 N

= 7 * 10^3 N which is wrong.

The motor needs to move both the boat and the skier. The boat is pulled with 7.50 * 10^4 W. What is the power of the force that moves the skier then?

ehild

 

[harts]

Another useful equation that would work in your case is

P=Fv

This comes from the fact that

P = ΔW/Δt = FΔx/Δt = Fv

 

[Parzival]

The motor needs to move both the boat and the skier. The boat is pulled with 7.50 * 10^4 W. What is the power of the force that moves the skier then?

ehild

Is it 83000 - 75000 = 1.2 * 10^4?

 

[ehild]

Is it 83000 - 75000 = 1.2 * 10^4?

It is 83000 - 75000, but not 1.2 * 10^4. Check the subtraction.

ehild

 

[Parzival]

It is 83000 - 75000, but not 1.2 * 10^4. Check the subtraction.

ehild

Fail. So 8.0 * 10^4?

 

[e^(i Pi)+1=0]

Another useful equation that would work in your case is

P=Fv

This comes from the fact that

P = ΔW/Δt = FΔx/Δt = Fv

interesting derivation

 

[harts]

Its not 8*10^4 either. That's, 80,000.

And.. thanks?

 

[Parzival]

Its not 8*10^4 either. That's, 80,000.

And.. thanks?

Fail. 8*10^3. Why thanks?

 

[ehild]

The skier is pulled at v=12 m/s speed by 8000 W power. What is the pulling force then?

ehild

 

[azizlwl]

deleting my post

 

[Parzival]

The skier is pulled at v=12 m/s speed by 8000 W power. What is the pulling force then?

ehild

So: 8000/12 N is the answer. Significant digits yield 6.7*10^2, which is correct!