Concept explainers
(a)
The magnitude of static frictional force exerted by road on each tire.
(a)

Answer to Problem 129P
The magnitude of static frictional force exerted by road on each tire is
Explanation of Solution
Consider Newton’s second law to find the force exerted by road on bicycle, since it is the only external force acting on bicycle.
Write the Mathematical expression for Newton’s second law
Here,
Both wheels of bicycle experience external force between road and wheel. Hence the expression for that force in terms of velocity is
Here,
Therefore, the expression of frictional force is
Conclusion:
Substitute,
Therefore, the magnitude of static frictional force exerted by road on each tire is
(b)
The
(b)

Answer to Problem 129P
The angular acceleration of two wheels is
Explanation of Solution
Write the expression for angular speed
Here,
Write the expression for angular acceleration
Here,
Conclusion:
Substitute,
Substitute
Therefore, the angular acceleration of two wheels is
(c)
The net torque acting on wheel.
(c)

Answer to Problem 129P
The net torque acting on wheel is
Explanation of Solution
Write the expression for net torque
Here,
Write the expression for moment of inertia
Here,
Substitute equation (VII) in (VI)
Conclusion:
Substitute,
Therefore, the net torque acting on wheel is
(d)
The normal force applied to a wheel by each of the brake pads.
(d)

Answer to Problem 129P
The normal force applied to a wheel by each of the brake pads is
Explanation of Solution
There are two components of net torque acting on each wheel, one is static friction force acting between road and wheel, and the other is the kinetic friction force acting on brake pads.
The direction of both forces will be opposite to each other. If the bicycle turns to right, static friction force will be in clockwise direction, and kinetic friction will be in counter clockwise direction.
Write the expression for net force in terms components
Rearrange equation (IX) to obtain expression for
Write the expression for normal force
Conclusion:
Substitute,
Substitute
Therefore, the normal force applied to a wheel by each of the brake pads is
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