A bike is moving with some velocity.There is some frictional force between the wheels of bike and ground.Now you apply brakes and the bike stops after some time.Brakes apply a force say F on wheels which slows down rotation of wheels,and finally wheels stop rotating.According to newtons 3rd law,wheels will also exert a force of equal magnitude on brakes (in the opposite direction of the force F).Thus,this reaction force on brakes gives momentum to bike (and this momentum is equal in magnitude to the loss of momentum due to slowing down rotation of wheels). Thus,momentum is conserved so bike would not lose its velocity but rotation of wheels is slowing down continuously.In that case,to obey the law of conservation of momentum, the bike would start sliding and sliding will be opposed by frictional force(between the wheels of bike and ground).This frictional force is the reason of losing momentum.My question is- is this possible that the reaction force on brakes gives momentum to bike (and this momentum is equal in magnitude to the loss of momentum due to slowing down rotation of wheels)? All suggestions are welcome.
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$\begingroup$ Well you are not considering losses due to heat generation on brakes and the heat lost to ground due to friction. $\endgroup$– Harshit JoshiCommented Nov 17, 2018 at 13:25
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1$\begingroup$ The law of conservation of momentum is only valid when no external forces act on the system. In this case, there is a brake force and a force due to friction so conservation laws are not valid. $\endgroup$– Harshit JoshiCommented Nov 17, 2018 at 13:28
1 Answer
In a bike-earth system while braking, if the system you consider is large enough, then any forces will be internal, not external.
Then consider this while braking.
A bike deccelerates from motion. The momentum of the bike is not conserved. However, when the road pushes the bike backwards due to friction, the bike wheels also push the road Earth in the opposite direction. So the car loses momentum to the right, while the Earth gains a momentum to the left that is equal in magnitude. So, due to this interaction*, the momentum of the bike-Earth system is not changed and the linear momentum is conserved. Of course the Earth has such a large mass that we do not notice the (extra) acceleration of the Earth due to the force exerted by the bike. (The Earth's mass is roughly 10^23 times greater than that of a bike, so the change in velocity of the Earth is smaller by that factor.)
