How to Calculate Work on an Inclined Surface?

In summary: But since we are not given the height we must find it using the angle of inclination and the distance traveled. So the next step would be to use trigonometry to find the height and then plug it into the equation for work, W=mg*h. In summary, the man does 6040 joules of work to pull the box 76 meters at an angle of 24 degrees. In the second part, the man must use trigonometry to find the height and then use the equation W=mg*h to calculate the work done to pull the box up the floor at a 10.6 degree angle.
  • #1
Iamaskier721
18
0

Homework Statement


A man pulls a 10 kg box across a smooth floor with a force of 87 Newtons at an angle of 24 degrees and for a distance of 76 meters. How much work, to the nearest joule, does he do?

If the floor in the previous question is angled upward at 10.6 degrees and the man pulls the box up the floor at constant speed what is the work he does to the nearest joule?


Homework Equations



W=f(cos theta)d

The Attempt at a Solution


The first part i achieved and got correct, which is 6040 j. I have no idea how to do the second part. Please help!
 
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  • #2
Since the speed is not changing, the work is equal to the change in gravitational potential energy. Actual distance doesn't matter, only the change in height.
 
  • #3
So it is being displaced 1.83 m veritcally. I Figured this out by the law of sines and a simple right triangle. What is the next step to solving this?
 
  • #4
Iamaskier721 said:
So it is being displaced 1.83 m veritcally. I Figured this out by the law of sines and a simple right triangle. What is the next step to solving this?

The work going into the change in gravitational potential is the weight times the height. In this case it is mg*h.
 

1. What is an inclined surface?

An inclined surface is a surface that is not horizontal, but rather at an angle or slope. This can be seen in ramps, hills, and even stairs.

2. How does work differ on an inclined surface compared to a horizontal surface?

On an inclined surface, the force of gravity still acts on an object, but it is now acting at an angle rather than straight down. This changes the work equation to W = Fd cosθ, where θ is the angle between the force and the displacement.

3. What is the relationship between the angle of incline and the amount of work done?

The amount of work done on an inclined surface is dependent on the angle of incline. As the angle increases, the amount of work done also increases. This is because the force of gravity is acting more perpendicular to the displacement, requiring more work to overcome it.

4. How does friction affect work on an inclined surface?

Friction can increase the amount of work needed to move an object on an inclined surface. This is because friction acts opposite to the direction of motion, meaning more work is needed to overcome it. This is why ramps and inclined planes are often used to reduce the amount of force needed to move an object.

5. Can work be negative on an inclined surface?

Yes, work can be negative on an inclined surface if the force and displacement are acting in opposite directions. This can happen when an object is sliding down an incline and the force of friction is acting in the opposite direction of motion. In this case, the work done by friction would be negative.

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