Are more wheels helpful?

Question

Suppose A motorcycle is coming down a slope. Only gravity is acting. If we put 2 wheels more in that motorcycle, will the speed increase or decrease compared to normal 2 wheels? If more wheels are helpful, why don't we attack two wheels to the back of motorcycles so that less force will be required and less accidents will occur?

Answer 1

Addition of two more wheels to the motorcycle that is coming down a slope would not change its speed.

If the slope makes an angle $\theta $ with the horizontal, then the net force acting on the motorcycle would be $ma = mg \sin \theta - \mu N $ where $\mu $ is the coefficient of friction, and $N = mg \cos \theta $ is the normal reaction. It is clearly evident that the mass would cancel out. So, the acceleration, and thus the velocity, does not depend on the mass. Frictional force does not depend on area of contact. So, the speed would remain the same as in the case of two wheels.

Addition of two more wheels does increase the stability. But, motorcycles are made for squeezing through small spaces. They cannot bend like at bends on race-tracks on addition of two more wheels. So, their main utility would be removed on addition of two more wheels. While practicing in cycles, two more wheels are fitted for practice and balance, but not in motorcycles.

Answer 2

It would go slower, for at least two reasons:

• Because of rolling resistance (see also this question); and
• because the lost gravitational potential energy would be converted in part into rotational kinetic energy of the extra wheels.

Also, as Wrichik points out, some of the advantages of a motorcycle can be lost with the addition of extra wheels.