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# Physics/Calculating work done by the gravitational force

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Question

Inclined plane
Dr. Stephen O. Nelson,

"How much work does the gravitational force acting on the skier represent if the skier travels 4 metres?"

As shown in the diagram in the attached image, the skier is moving downwards on a slope, which represents parallel direction of the skier. Now I will proceed to show my steps that I have done so far.

1. Since the mass of the skier is 70 kg, I used the formula to calculate its weight:

weight = (mass)(gravitational field intensity)
= (70kg)(9.8N/kg)
= 686N
= 700N (since I have to round the result to 1 significant figure)
2. I'm guessing though that I should keep my original result from step 1 (686N) for step 2. So then I used the formula to calculate the work done by the skier (I'm assuming it is done by the skier):

work= (force or force component parallel to direction of travel)(distance)
= (686N)(4m)
= 2744J
= 3000J (rounded to 1 significant figure)
So the work done by the skier is 3000J.
But I interpreted from the question that I need to calculate the amount of work done by the gravitational force.

3. Therefore, to calculate the gravitational force (blue arrow in diagram), I used trigonometry within the large triangle:

sin (15°) = x/686N
x = 178N (rounded to 3 significant figures)

OR should have I used trigonometry in the smaller triangle?

sin (15°) = 686N/x
= 2660N (rounded to 3 significant figures)

So now I'm stuck because I know that 4m is used in the formula to calculate the work done by the skier but I'm unsure if 4m also applies to the gravitational force.

To calculate the work done by the gravitational force:

work = (force or force component // to direction of travel)(distance)
= (2660N)(4m)
= 10640J
= 10000J (rounded to 1 significant figure)

So I calculated the work done by the gravitational force to be 10000J but when my class was going over the answers, I heard 7J. 10000J and 7J are very different from each other so I'm wondering if I either miscalculated anything or if I just misheard them saying the answer?
Thank you in advance for your time and help in clarifying any possible mistakes.

Answer
Normally I don't touch homework problems, but this one you did try yourself and it's an easy fix.  You mixed up your components when you chose 2660N instead of 178N.  How do I know?  A component of a force will only ever be a part of a force.  If you used a component and got something larger than the original, you divided where you should've multiplied.  Try thinking of these component problems in this way, if components confuse you...since gravitation is only a vertical force, then you need the vertical distance that he went along that force (down).  You can use the component of force (178N) along the total distance (4m) if you want, but I think that's a reverse way to think of it.  He went down a distance of 4m(sin15)=1.03m, and the total vertical work done is 686N*1.03m=710J.  The other way is to think of the component of gravity multiplied by the distance, it just puts the sin15 in with the weight (178N*4m)=710J.  Either way, the answer is the same, and neither is wrong...but there's usually two ways to think out the answers to these problems.  The right way is the one that makes the calculations make sense.  I do the same thing with torques, I think about the perpendicular distance of the lever arm and not the component of the force...but you won't get to that until rotation.  Good luck.

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#### Dr. Stephen O. Nelson

##### Expertise

I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

##### Experience

I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

Education/Credentials
Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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