Power/Work-Energy HW: Find Tension in Ski Boat Tow Rope

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AI Thread Summary
The discussion focuses on calculating the tension in the tow rope of a ski boat pulling a skier. The motor generates an average power of 8.30 * 10^4 W when pulling the skier at a constant speed of 12 m/s. The initial calculations for force were incorrect, leading to confusion over the correct subtraction of powers. The correct power used to find the tension is derived from the difference between the two power outputs, resulting in 8000 W for the skier. Ultimately, the tension in the rope is calculated to be approximately 6.7 * 10^2 N.
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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.
 
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Parzival said:
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
 
Another useful equation that would work in your case is

P=Fv

This comes from the fact that

P = ΔW/Δt = FΔx/Δt = Fv
 
Last edited:
ehild said:
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?
 
Parzival said:
Is it 83000 - 75000 = 1.2 * 10^4?

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

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

ehild

Fail. So 8.0 * 10^4?
 
harts said:
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
 
Its not 8*10^4 either. That's, 80,000.

And.. thanks?
 
harts said:
Its not 8*10^4 either. That's, 80,000.

And.. thanks?


Fail. 8*10^3. Why thanks?
 
  • #10
The skier is pulled at v=12 m/s speed by 8000 W power. What is the pulling force then?

ehild
 
  • #11
deleting my post
 
  • #12
ehild said:
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!
 
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