How Does Static Friction Affect Bicycle Acceleration?

[7.11brown]

Homework Statement

Consider a biker riding on level ground as shown. She wants to have the maximum forward acceleration possible, which means experiencing the maximum horizontal force without her wheels slipping. Draw the free body diagram for the bike accelerating forward.

Homework Equations

F=ma
kinetic friction is zero

The Attempt at a Solution

there would be weight going down from each wheel (dependent on the balance of the rider), a Normal Force from each going up, rolling friction on the front wheel and static friction in the direction of acceleration on the rear wheel

Is that correct? Would the force of static friction only be dependent on the weight the rider puts on the rear wheel?

 

[LawrenceC]

The force of friction would also depend on how much the center of gravity shifts to the rear when she accelerates. For example suppose when not accelerating the bike/rider has a 50/50weight distribution. But when it accelerates, the CG shifts rearward which increases the weight on the rear wheel. It could then be 60/40 or some other ratio.

 

[7.11brown]

Just to make sure, my description of the free body diagram looked correct? If so, when calculating the frictional force, it would just be equal to the y component of weight on the rear wheel (assuming rolling friction is negligible.)? We are assuming a 50/50 weight distribution.

When using F=ma to find the acceleration of the bike and rider, would that mass be equal to the total mass since that is what is accelerating?

Thanks

 

[LawrenceC]

"there would be weight going down from each wheel (dependent on the balance of the rider), a Normal Force from each going up, rolling friction on the front wheel and static friction in the direction of acceleration on the rear wheel"

Since you mention the weight going down and the normal force from pavement going up on each wheel, shouldn't you also mention the propulsion force that equals the friction force due to weight on rear wheel times coefficient of friction? Also in this vein, should you mention both forward and backward forces on front wheel. Don't forget, the front wheel is accelerating angularly so there is a torque term (due to angular acceleration) that equals the friction term.

"When using F=ma to find the acceleration of the bike and rider, would that mass be equal to the total mass since that is what is accelerating?"

Absolutely. It's the rider's mass plus the mass of bicycle.

 

[asteriatic]

Your free body diagram is correct. The weight and normal forces will cancel out in the vertical direction, leaving only the horizontal forces to consider. The rolling friction on the front wheel will be in the opposite direction of the acceleration, while the static friction on the rear wheel will be in the same direction as the acceleration. The magnitude of the static friction force will depend on the weight distribution and balance of the rider, as well as the coefficient of static friction between the rear wheel and the ground. The maximum forward acceleration can be achieved when the static friction force reaches its maximum value without causing the wheels to slip. This can be achieved by adjusting the weight distribution and maintaining a proper balance on the bike.