Calculating Work to Pull a Skier Up a Slope at Constant Speed

In summary, the problem involves a skier being pulled up a 30.1° slope at a constant speed of 2.07 m/s. The force of gravity parallel to the slope is calculated as 341.57 N and the total negative work done is 20.186 kJ over a distance of 59.1 m. The given velocity of 2.07 m/s is not a factor in this calculation, as Newton's Second Law states that the forces must be equal for a constant speed. Therefore, the required work to pull the skier up the slope is still 20.186 kJ, regardless of the velocity at which they are pulled.
  • #1
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Homework Statement


A skier of mass 69.5 kg is pulled up a slope by a motor-driven cable.
a) How much work is required to pull him a distance of 59.1 m up a 30.1° slope (assumed frictionless) at a constant speed of 2.07 m/s?


The Attempt at a Solution


I started out this problem by finding out what that force of gravity parallel to the slope would be.
mgsin(30.1)=341.57 N

Then I figured I would find the total negative work that would be done for the whole slope so I multiplied that by 59.1m to get 20.186 kJ.

The thing I am not sure how to figure out is how much work is required to pull him up at 2.07 m/s. Because anything greater than 20.186kJ would just pull him up, but not necessarily at 2.07 m/s.

Also this answer alone counts as the right answer, but it can't be exactly right because its hasn't taken into account the desired velocity right?
 
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  • #2
You did the problem absolutely right, the 2.07 m/s was just thrown in there to trick you. Because it is at a constant speed, Newtons Second Law says the forces must be equal. The 2.07 was an arbitrary value that the skier is brought to before the incline, it could have been 1000 with the same result.
 
  • #3
I kind of had the inclination the whole time. So, it wouldn't matter what velocity he was traveling it would still be the same joules?
 

1. How do you calculate the work required to pull a skier up a slope at constant speed?

The work required to pull a skier up a slope at constant speed can be calculated using the formula W = F * d, where W is the work, F is the force applied, and d is the distance over which the force is applied.

2. What units are used to measure work in this scenario?

The SI unit for work is joule (J). In this scenario, work can also be measured in Newton-meters (N*m) or kilogram-meters squared per second squared (kg*m^2/s^2).

3. Is the work required to pull a skier up a slope at constant speed affected by the weight of the skier?

Yes, the work required to pull a skier up a slope at constant speed is affected by the weight of the skier. The greater the weight of the skier, the more work is required to pull them up the slope.

4. How does the angle of the slope affect the work required to pull a skier up at constant speed?

The steeper the slope, the more work is required to pull a skier up at constant speed. This is because the force required to counteract the force of gravity increases as the angle of the slope increases.

5. Can you calculate the work required to pull a skier up a slope at constant speed using only the mass and speed of the skier?

No, the work required to pull a skier up a slope at constant speed cannot be calculated using only the mass and speed of the skier. The distance over which the force is applied is also needed in order to calculate work.

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