Question

The distance between the centers of the wheels of a motorcycle is 146 cm. The center of mass ofthe motorcycle, including the rider, is 78.5 cm above the ground and halfway between the wheels.Assume the mass of each wheel is small compared to the body of the motorcycle. The enginedrives the rear wheel only. What horizontal acceleration of the motorcycle will make the frontwheel rise off the ground

Answer 1

Answer:

9.12267515924 m/s²

Explanation:

Here the moment created by the wheels and the moment created by the center of gravity will balance each other.

h = Height of the center of mass = 78.5 cm

d =  Distance from back wheel to the center of mass = $\dfrac{146\times 10^{-2}}{2}\ m$

g = Acceleration due to gravity = 9.81 m/s²

a = Horizontal acceleration

The equation is of the form

$mgd=Fh\\\Rightarrow mgd=mah\\\Rightarrow a=\dfrac{gd}{h}\\\Rightarrow a=\dfrac{9.81\times \dfrac{146\times 10^{-2}}{2}}{78.5\times 10^{-2}}\\\Rightarrow a=9.12267515924\ m/s^2$

The horizontal acceleration of the motorcycle that will make the front wheel rise off the ground is 9.12267515924 m/s²