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When I ride my bike, does half of the energy go into the earth because of Newton's third law? Does the energy in the earth transfer into heat upon my brakes when I utilize them?

If the earth was 2000 times less massive than it is, and I applied the same energy to my pedal, would my bike move (relative to an observer not connected to earth) at the same speed as it would if the earth was normal?

I think if you think about it these two questions are the same.

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Hi Velox. Your bike won't waste any fuel for earth. Because the contact force is provided by the weight itself. And, What do you mean by the phrase, energy in the earth... ? – Waffle's Crazy Peanut Mar 8 '13 at 3:04
related and correct physics in the answer by @Joshphysics at… – anna v Mar 8 '13 at 7:37
up vote 2 down vote accepted

No, because even though the force that you exert on the earth is equal and opposite to the force it exerts back on you, you're not doing the same amount of work on the earth as the earth on you. Your kinetic energy increases due to the work done by the earth on you. Remember that $W = F \cdot d$; your bicycle moves a lot due to this force, but the earth doesn't really move much at all.

Another way to think about this is in terms of kinetic energy. $\mathrm{KE} = \frac{1}{2} mv^2$, so if your velocity is high, so is your kinetic energy. The earth's velocity is low, and so is its kinetic energy. So the forces are equal and opposite, and the impulse, or change in momentum, is too, but the kinetic energy stays mostly with you.

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Hi @krs013, and welcome to physics.SE! In case you didn't know, we have Latex-style markup enabled, as I've edited into your answer. (Not that it's strictly necessary for such short equations, but it's there in case you want it.) – Chris White Mar 8 '13 at 4:58
Thanks! I was wondering about that. I was needing it for another answer too. – krs013 Mar 8 '13 at 5:25

I think you are confusing momentum and energy.

If you ignore air friction then it would take almost no energy to cycle in a vacuum, just the energy to overcome friction in the wheel bearings (well that and the inability to breath)

Cycling at reasonably quick speeds most of the energy goes into aerodynamic drag, that is moving the air out of the way, and so ultimately to heat in the air.

Yes - when you brake all the kinetic energy goes into the brake pads which is then dissipated into the air as the pads heat up

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you are ignoring friction of the bike wheels on the ground, without which no transport can happen, and also ignoring angular momentum induced on the earth, extremely small but calculable. . see also connected answer by Joshphysics… – anna v Mar 8 '13 at 5:20
Is there any work done by the friction of the wheels on the ground ? - there is a force but no movement. There are friction loses in the tyres due to compression and expansion of the rubber but there shouldn't be in the road contact unless you are skidding. – Martin Beckett Mar 8 '13 at 5:31
if there were no work you would be skidding, imo Have a look at the figure in wiki – anna v Mar 8 '13 at 5:35
Think of a large turn table, motionless. Ride a bicycle close to the periphery. What will happen? – anna v Mar 8 '13 at 6:13
@annav - good point I was thinking there was a momentum transfer but not energy – Martin Beckett Mar 9 '13 at 4:21

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