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M2 - Work and Energy

I'm stuck on how to work out this question. Tips?

A girl and her sledge have a combined mass of 40 kg. She starts from rest and descends a slope which is inclined at 2525^\circ to the horizontal. At the bottom of the slope the ground becomes horizontal for 15m before rising at 66^\circ to the horizontal. The girl travels 25m up the slope before coming to rest once more. There is a constant resistance to motion of magnitude 18N. Calculate the distance the girl travels down the slope.
(edited 13 years ago)
ViralRiver
I'm stuck on how to work out this question. Tips?

A girl and her sledge have a combined mass of 40 kg. She starts from rest and descends a slope which is inclined at 2525^\circ to the horizontal. At the bottom of the slope the ground becomes horizontal for 15m before rising at 66^\circ to the horizontal. The girl travels 25m up the slope before coming to rest once more. There is a constant resistance to motion of magnitude 18N. Calculate the distance the girl travels down the slope.


Assume the distance travelled down the slope is "x".

What's the loss in energy between beginning and end?

What's the work done?

Equate. Solve.

(edited 13 years ago)
Reply 2
Hmm, I already used x for that and *tried* solving, but ehh I didn't know what to do. I equated x=25sin67201840gsin25x = \frac{-25sin6-720}{18-40gsin25} but the answer isn't correct.
ViralRiver
Hmm, I already used x for that and *tried* solving, but ehh I didn't know what to do. I equated x=25sin67201840gsin25x = \frac{-25sin6-720}{18-40gsin25} but the answer isn't correct.


So what was your original equation, before you started rearranging it?

It should be based on:

Loss in GPE = work done.
(edited 13 years ago)
Reply 4
I worked out the loss in EP, which was =40gxsin2525sin6 = 40gxsin25-25sin6. Then I knew that work done = force x distance so distance=25+15+x=40+x=40gxsin2525sin618distance = 25 + 15 + x = 40 + x = \frac{40gxsin25-25sin6}{18}.
ViralRiver
I worked out the loss in EP, which was =40gxsin2525sin6 = 40gxsin25-25sin6. Then I knew that work done = force x distance so distance=25+15+x=40+x=40gxsin2525sin618distance = 25 + 15 + x = 40 + x = \frac{40gxsin25-25sin6}{18}.


Loss in GPE

=40g(xsin2525sin6) = 40g (xsin25-25sin6)
(edited 13 years ago)
Reply 6
Ahh, silly mistake. Thanks :smile: .
Reply 7
Silly mistakes are the story of my M2, I mean it's not that difficult I just don't have the raw concentration :frown:
Original post by ghostwalker
So what was your original equation, before you started rearranging it?

It should be based on:

Loss in GPE = work done.


Why don't we care about the change in KE?

I completely overthought this question.
I thought you had to find the velocity before going up 6 degree which allows you to find the velocity to find the velocity before becoming horizontal which allow you to find the distance travelled in the first slope using increase in KE = fall in gpe + WD agaisnt resistance
Original post by creativebuzz
Why don't we care about the change in KE?

I completely overthought this question.
I thought you had to find the velocity before going up 6 degree which allows you to find the velocity to find the velocity before becoming horizontal which allow you to find the distance travelled in the first slope using increase in KE = fall in gpe + WD agaisnt resistance


We treat the whole motion from start to finish in one go.

KE at start = 0
KE at end = 0

No change.

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