Physics of Stopping a Bike

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Recommended: Conservation of Momentum investigation

In short brakes are a tool that turn kinetic energy into heat(http://en.wikipedia.org/wiki/Brakes). This is accomplished by applying friction in one way or another. In the case of disk brakes friction is created because the braking mechanism exerts a force on the break pads which pushes them into contact with disk. It is this contact combined with the fact that the disks are rotating that causes kinetic energy to be converted to heat.

If the purpose of brakes is to convert kinetic energy into heat, then in order to know how much heat the brakes make requires that we find out how much kinetic energy there is in a moving bicycle.

The important thing to know about an object that is moving on wheels is that its kinetic energy is equal to half of its mass including the wheels(Mb) multiplied by the square of its velocity(V) plus the kinetic energy in the rotating wheels. In this case I am going to assume that all of the mass of the wheels is located on the outer edge (this isn't really the case, but most of the mass is there). Then the kinetic energy of a wheel due to rotation is half of its mass(Mw) multiplied by the square of its radius(r) multiplied by the square of its angular velocity(w) multiplied by two since there are two wheels.

kinetic energy of the bicycle = ½MbV2 + 2½Mwr2w2

Since the velocity of an object rolling on wheel(s) is equal the radius of the wheel times its angular velocity we can substitute V2 in for r2w2. This substitution leaves us with:

kinetic energy of the bike = V2(Mw+½Mb).

I mentioned on the last page that we must stop the bike by turning its kinetic energy into friction. To do this, the brakes apply a force to the disk with pads. The force of this friction is equal to the total downward force (f) that the pads put on the disk(the pads are usually on each side of the disk and crush it between them) multiplied by the coefficient of friction(u).

force of friction = (f)(u)

For our purposes, while a bike is coasting the only things besides pedaling that can effect its speed are the force of friction from the brakes and gravity.

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