The distance between the centers of the wheels of a motorcycle is 169 cm. The center of mass of the motorcycle, including the rider, is 77.0 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 engine drives the rear wheel only. What horizontal acceleration of the motorcycle will make the front wheel rise off the ground?
m/s2
this question is poorly worded and cannot be done
To find the horizontal acceleration that will make the front wheel rise off the ground, we need to consider the conditions for static equilibrium. When the front wheel is just about to leave the ground, the net torque acting on the motorcycle must be zero.
We can start by identifying the forces and torques acting on the system. The forces on the motorcycle are the weight (acting downward), the normal force from the ground (acting upward), and the force of friction (acting in the opposite direction of motion).
Considering the torques, the weight of the motorcycle and the rider acts at the center of mass, so it does not create any torque. The normal force and the force of friction also do not create any torque since their line of action passes through the center of mass.
When the front wheel is about to lift off, the normal force becomes zero. So, the weight is balanced by the force of friction.
The frictional force can be calculated as:
frictional force = coefficient of static friction * normal force
Since the front wheel is just about to lift off, the normal force is zero. Therefore, the frictional force is zero as well.
Now, let's consider the horizontal forces. The net force acting on the motorcycle is provided by the engine, and it generates acceleration.
Using Newton's second law, we can relate the net force and acceleration:
net force = mass * acceleration
Since the net force is zero (due to the frictional force being zero), the acceleration is also zero.
So, the horizontal acceleration that will make the front wheel rise off the ground is zero m/s^2.