Skiing Up a Slope: Solving Work & Power Requirements

[komarxian]

Homework Statement

A skier of mass 70 kg is pulled up a slope by a motor-drive cable.
a. How much work is required to pull him 60 m up a 30° slope (assumed frictionless) at a constant speed of 2 m/s?
b. What power must a motor have to perform this task?

Help would be greatly appreciated!

Homework Equations

The Attempt at a Solution

I will be attaching pictures in a reply to this in a minute, and these pictures will have my work. I have no idea if I did it correctly, as my textbook does not have an answer for this proble, but I don't feel totally clueless, so that's good?
The thing is, there's no acceleration, so it's kind of confusing, because the normal W= Fd doesn't seem to work because I keep getting 0 N, because a=0, but when I solve using ΔU, I actually get something, but once again, I have no clue if it is correct. Any help is greatly appreciated!

 

[komarxian]

My attempt!

 

[haruspex]

As you rightly observe, the constant speed means no work is done on the skier. All the work is done against gravity, and PE is the way to figure that out.
But you seem to have some mistakes in your calculations. Where does the 35 come from?
What force does your F represent? I assume it is the tension in the cable. Over what distance does that force haul the skier?

 

[komarxian]

35 comes from my sine calculation for the height of the slope. I will reloik at the problem about the tension, thanks!

 

[haruspex]

35 comes from my sine calculation for the height of the slope.

Then I suggest you work it out again.

 

[komarxian]

Okay got it.

 

[komarxian]

Okay here is my work! The problem I solved for was #48 and my answer is 700 Watts?

 

[haruspex]

Okay here is my work! The problem I solved for was #48 and my answer is 700 Watts?

Yes. Quickest way is to note that 2m/s up a 30 degree slope is 1m/s vertically, so power = mass x g x 1m/s.

 

[NascentOxygen]

@komarxian Please post future images right-way up for viewing. Readers find screens exceeding around 42" are all but impossible to wrench around 90° and balance on their end.

Images are considerably more difficult to read than is rendered text, particularly in less than favourable lighting. For this reason we ask that you learn to present your working using Latex, and reserve images for just the labelled diagrams.

 

[komarxian]

Okay! I'll try that out.