GCSE Physics- Energy & Efficiency question

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ElderFupaMaximus
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#1
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#1
I'm having a tough time figuring out question 1c. Does anyone know how to do it?

-->(A car of mass 1,000 kg begins stationary on a road at the top of a mountain, at a height h = 3,000 m. The car then rolls freely down a winding road, traveling a total distance of 5 km, to reach the height h = 2,000 m. Assume g = 9.8 ms-2)

1a. How much energy did the car lose on descent? Give your answer to 3 significant figures, with units.
Ans: Energy lost = 9,800,000 J.
1b. At this point, how much energy is stored in a gravitational potential store? Give your answer in kJ.
Ans: GPE = 19,600 kJ.
1c. The car continues to roll down the mountain, where it reaches the bottom. Here the height h = 0 m. Assuming no further energy is lost and all the GPE from the top of the mountain is transformed into KE, what is the final velocity of the car? Give your answer to 3 significant figures.
Ans: Final velocity = ___ms-1
Last edited by ElderFupaMaximus; 1 year ago
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riddhi.78
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Potential Energy at the top = Kinetic Energy at the bottom
Loss in PE = Gain in KE
mgh = 1/2 mv2
gh= 1/2 v2 (upon dividing both sides by common factor m or striking it off)
9.8 X 3000 = 0.5 v2
v2 = 58800
v = 242. 49M/S

Is that it? If not, then the answer accounts for the energy loss
Hope this helps u
Last edited by riddhi.78; 1 year ago
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Joinedup
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All the GPE is converted to KE
Seems that you have a value for the amount of GPE converted so you just have to rearrange the formula for KE
KE = 1/2 m v^2
a bit
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ElderFupaMaximus
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Thank you!
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Fliw42
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Wait how to you do a and b?
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ElderFupaMaximus
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(Original post by Fliw42)
Wait how to you do a and b?
To find the GPE you need to know the formula, which is:
GPE=mgh
or
Gravitational Potential energy= mass x gravitational filed strength x changing height.

For part a, we simply use the information given in the question.
1. Substitute the formula GPE=mgh --> GPE= 1,000kg x (3,000m-2,000m) x 9.8 ms-2= 9,800,000J

Since we figured out the energy lost in part a, to work out part b, all we need to do is find the initial energy, take the energy lost away from it and convert J to kJ.
1. Substitute the formula: GPE=mgh --> GPE= 1,000kg x 3000m x 9.8 ms-2= 29,400,000J
Notice how this time we only use the initial height, this is because we only want to know the initial energy.
2. Now find the energy left using subtraction: 29,400,000J - 9,800,000J= 19,600,000J
3. Finally, we need to convert J to kJ. This can be done by doing 19,600,000J x (1/1000)= 19,600kJ
The 1/1000 is the scale factor that converts J to kJ.
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Fliw42
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Thankyou!!!
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ElderFupaMaximus
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(Original post by Fliw42)
Thankyou!!!
No problem!
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17ewebb
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#9
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what is the final velocity?
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Lilsmileyfaceman
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been a year. did you find out yet? like.. seneca is really messing with me bruh.
Last edited by Lilsmileyfaceman; 3 months ago
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Driving_Mad
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#11
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(Original post by Lilsmileyfaceman)
been a year. did you find out yet? like.. seneca is really messing with me bruh.
All the GPE is transferred to KE as the energy transfer is 100% efficient (no air resistance).

This means you can set the GPE lost = KE gained

So calculate the GPE lost (hint: height car falls is 3000m), and set it equal to 0.5 * mass * speed^2, rearranging to find speed.

(There is a quicker way but this is the easiest way I think to explain it).
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