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1. I have a question that I have successfully answered after two attempts, however there is something I am confused about.

The question:

A boy and his skateboard have a mass of 50 kg. He descends a slope inclined at 12 degrees to the horizontal starting from rest. At the bottom, the ground becomes horizontal for 10m before rising at 8 degrees to the horizontal. The boy travels 30m up the incline before coming to rest again. He is subject to a constant resistance of 20N throughout the motion. By modelling the boy and his skateboard as a single particle find the distance the boy travelled own the slope.

The solution I happened to have used (borrowed from Chaoslord in another thread):

use mgh

by using change in height you find the energy wasted in friction

so change in height = Xsin12 - 30sin8

and distance traveled = 40 + X

now force x distance = work done = change in energy

we can model the change in energy by using (Xsin12 - 30sin8) x 9.8 x 50

and work done due to friction is (40 + X) x 20N

then equate to find X
I have made bold my question. If we assume change in height to be Xsin12 - 30sin8 then surely we are also assuming that the initial height is greater than the ending height?

Using 30sin8 - Xsin12 instead, ends up getting a wrong answer, and I presume this is because we need a POSITIVE change in height, to work out a POSITIVE change in energy? Or is it to do with the fact, that if the only force acting is gravity, then the initial height cannot be less than the end height?

I'm confused.
2. (Original post by cazmasetro)
I have a question that I have successfully answered after two attempts, however there is something I am confused about.

The question:

A boy and his skateboard have a mass of 50 kg. He descends a slope inclined at 12 degrees to the horizontal starting from rest. At the bottom, the ground becomes horizontal for 10m before rising at 8 degrees to the horizontal. The boy travels 30m up the incline before coming to rest again. He is subject to a constant resistance of 20N throughout the motion. By modelling the boy and his skateboard as a single particle find the distance the boy travelled own the slope.

The solution I happened to have used (borrowed from Chaoslord in another thread):

I have made bold my question. If we assume change in height to be Xsin12 - 30sin8 then surely we are also assuming that the initial height is greater than the ending height?

Using 30sin8 - Xsin12 instead, ends up getting a wrong answer, and I presume this is because we need a POSITIVE change in height, to work out a POSITIVE change in energy? Or is it to do with the fact, that if the only force acting is gravity, then the initial height cannot be less than the end height?

I'm confused.
No initially he descends X metres down the slope at an angle of 12 degrees so the height is Xsin12, then he rises 30 metres at an angle of 8 degrees so that's 30sin8.

The change in height from his original position to where he is now would be the height he descends take away the height he rises.

Therefore Xsin12 - 30sin8 is the change in height

3. (Original post by Boy_wonder_95)
No initially he descends X metres down the slope at an angle of 12 degrees so the height is Xsin12, then he rises 30 metres at an angle of 8 degrees so that's 30sin8.

The change in height from his original position to where he is now would be the height he descends take away the height he rises.

Therefore Xsin12 - 30sin8 is the change in height

Hi, thanks for replying

So, what if the height he rises is larger than the height he descends? Is that not possible? Because if it were, surely you would get a negative answer... Does mgh always have to be positive, since energies are not vectors?

If I'm correct,

work done by cyclist = work done against resistances + change in energy

is that right?
4. (Original post by cazmasetro)
Hi, thanks for replying

So, what if the height he rises is larger than the height he descends? Is that not possible? Because if it were, surely you would get a negative answer... Does mgh always have to be positive, since energies are not vectors?

If I'm correct,

work done by cyclist = work done against resistances + change in energy

is that right?
If the height he rises is larger than that means he gains energy as there's an increase in GPE. So no you cannot have negative energy, a negative answer would just mean its in the opposite direction.

Hmm does the question give you any info on KE?
If not I believe that's correct.

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