# Find work done pulling sled with rope

• ObviousManiac
In summary, the homework statement states that a loaded sled is pulled by means of a rope that makes an angle of 45 degrees with the horizontal. If the mass of the sled is 60 kg and the coefficient of friction is .0200, then 16,305 J of work is done in pulling the sled at constant velocity along a level road for a distance of 1.00 km.
ObviousManiac

## Homework Statement

A loaded sled is pulled by means of rope that makes an angle of 45 with the horizontal. If the mass of the sled is 60 kg and the coefficient of friction is .0200, how much work is done in pulling the sled at constant velocity along a level road for a distance of 1.00 km?

## Homework Equations

Problem solved here:

http://www.flickr.com/photos/landolukes/5831482036/lightbox/"

## The Attempt at a Solution

My final answer is 16,305 J. Yet, My teacher got 11,541 J. My tutor says I did it right, so I thought I'd bring it here for some other opinions.

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It's definitely 11,541 J. Don't forget the contribution to the normal force from the vertical component of the applied (pulling) force.

EDIT: In your work, it looks like you forgot that only the component of Fapplied that is parallel to the displacement of the sled does any work (i.e. only the x-component does work). So you are missing a factor of cos(45°) from the final answer.

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This may be a dumb question, but wouldn't it be 11,772 J?

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nayfie said:
This may be a dumb question, but wouldn't it be 11,772 N?

Without seeing any work, I can't really comment further. How did you arrive at that answer? I'm more than happy to show what I did, if you like.

$W = F \bullet s$

There is no displacement in the vertical axis, therefore $W_{y} = 0$

$F = F_{friction} = \mu F_{N} = (0.02)(60*9.81) \approx 11.772$

$W_{x} = F \bullet s = |F||s|cos\theta = (11.772)(1000)cos0 \approx 11,772$ J

Your error comes in the third line where you assume that FN = mg. The normal force is slightly less than the weight, because the person is pulling upward on the box with a vertical force equal to Fsinθ. Hence, the magnitude of the normal force is mg - Fsinθ.

Oh yes! How obvious...

Thank you :)

## 1. How do you calculate the work done while pulling a sled with a rope?

The work done while pulling a sled with a rope can be calculated using the formula W = F x d, where W is the work done, F is the force applied, and d is the distance the sled is pulled. This formula assumes that the force is constant and in the same direction as the displacement.

## 2. What factors affect the amount of work done while pulling a sled with a rope?

The amount of work done while pulling a sled with a rope is affected by several factors, including the force applied, the distance the sled is pulled, and the angle between the force and the direction of displacement. Other factors such as friction and the weight of the sled may also impact the work done.

## 3. How does the angle between the force and the direction of displacement affect the work done while pulling a sled with a rope?

The angle between the force and the direction of displacement affects the work done by reducing the amount of work done when the force is not applied in the same direction as the displacement. This is because only the component of the force in the direction of displacement contributes to the work done.

## 4. Can you use the same formula to calculate work done when pulling a sled with different types of ropes?

Yes, the formula W = F x d can be used to calculate the work done while pulling a sled with any type of rope. However, the force applied may vary depending on the type of rope used, as well as other factors such as the tension and elasticity of the rope.

## 5. How can you increase the work done while pulling a sled with a rope?

To increase the work done while pulling a sled with a rope, you can increase the force applied or the distance the sled is pulled. Additionally, reducing the angle between the force and the direction of displacement can also increase the work done. However, factors such as friction and the weight of the sled may limit the amount of work that can be done.

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