Physics Work, Force, Energy problem

[Quinton Lutz]

What force did the child exert if he got to the top of the slide by climbing up the 10 meter long side of the slide?
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpa1/v/t34.0-12/10863755_1035352396481600_499412383_n.jpg?oh=e7ad2ad952d3fdca760ac98ed1b59ebe&oe=548F4670&__gda__=1418653456_ac219d3a189cf6d15b47ccb70de90f1f
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpa1/v/t34.0-12/10846976_1035352363148270_1792159887_n.jpg?oh=cb662a069afbf224b2750559d8a17b46&oe=548EE155&__gda__=1418659460_f3d5a9eef0c9baa2ccdb7d0c055a6d88 W = F*X, X=displacement
Esubk = (.5)m*v^2

I simply subbed in the 700J for the work, used 3m as the displacement and solved the equation for F.
My classmates have been solving this using 10m instead of 3m. I am unsure of what the correct solving process for this is. My answer was 200 using only one significant figure.

 

[Nathanael]

How is displacement defined? The child starts at the bottom of the slide and ends at the top of the slide; what is the child's displacement?

P.S.
It is probably against the rules to post a poll with the answers on it, because the point of this part of the forums is to help people to understand the solution, not to simply give them the answer.

 

[Quinton Lutz]

Well, as far as I am aware, when calculating work, displacement and force should normally be directional, so to find work of walking up a stair case, you would us the height of the stairs multiplied by the gravitational force acting on your self (weight). I am confused on whether it is possible to use the diagonal displacement shown or if you are to use the vertical displacement?

 

[Nathanael]

You can use the diagonal displacement and the component of the gravitational force acting parallel to the slide. The normal force from the slide balances the other component of gravity so you only have to push against part of the gravitational force.

If you were to lift the child vertically up 3 meters, then you would be opposing the entire force of gravity. But if you were to push the child up the slide, you would only be opposing part of the force of gravity (the component parallel to the slide) and (ignoring friction) it would be "easier" to do (less force would be required).

So yes, you can use the diagonal displacement, as long as you don't use the entire force of gravity. (As you hinted at, you would only use the component of gravity which is in the same direction as the diagonal displacement.)P.S. Your method for finding the work done climbing the stairs (and for climbing the slide) is correct. But the problem didn't ask for the work done, it asked for the force.

 

[haruspex]

My answer was 200 using only one significant figure.

That's a bit inaccurate because you've already lost precision in computing the number of Joules.
If you go back to an algebraic expression for the work done (instead of subbing in numbers) then get the algebraic expression for the force you should notice something.

 

[ehild]

The question is poorly formulated. What force did the child exert - on what?
Did it exert no force perpendicularly to the slope?
Is it possible to walk up on a frictionless slope?
How can we walk at all? Do we need zero horizontal force to move horizontally?
The answer would be easy, if the child pulled itself up with the help of a rope fixed to the top of the hill .