Motorcycle Wheels: Calculating Horizontal Acceleration for Front Wheel Lift Off

[pradeepk]

Homework Statement

The distance between the centers of the wheels of a motorcycle is 155 cm. The center of mass of the
motorcycle, including the rider is 88 cm above the ground and halfway between the wheels. Assume that the mass of
the wheels is small compared to the body of the motorcycle. The engine drives only the rear wheel. What horizontal
acceleration of the motorcycle will cause the front wheel to rise off of the ground?

Homework Equations

The Attempt at a Solution

I'm not sure how to begin this problem. I'm trying to grasp the concept but I am not too sure. So the back wheel of the motorcycle causes a torque on the front wheel which causes it to rotate? Any help would be appreciated, thank you.

 

[berkeman]

Homework Statement

The distance between the centers of the wheels of a motorcycle is 155 cm. The center of mass of the
motorcycle, including the rider is 88 cm above the ground and halfway between the wheels. Assume that the mass of
the wheels is small compared to the body of the motorcycle. The engine drives only the rear wheel. What horizontal
acceleration of the motorcycle will cause the front wheel to rise off of the ground?

Homework Equations

The Attempt at a Solution

I'm not sure how to begin this problem. I'm trying to grasp the concept but I am not too sure. So the back wheel of the motorcycle causes a torque on the front wheel which causes it to rotate? Any help would be appreciated, thank you.

Fun problem! (Note my avatar...)

Draw a FBD of the motorcycle, showing the rigid body consisting of the back wheel and the CM of the bike. The torque to balance the CM will cause some angular acceleration of the rear wheel, which will cause some horizontal acceleration of the bike.

My first instinct is that the radius of the rear wheel should enter into the calculations, but maybe it cancels out...

Please show your work...