A car weighing 1.07 x 10^4 N is at rest on a 32.5° incline. Each wheel bears an equal part of the car's weight. Thus the axles apply a vertical downward force of 2.68 x 10^3 N to the center of each wheel. (a) Find the frictional force exerted by the road on each wheel (b) Find the sum of the magnitudes of the frictional forces fB applied by the brakes to the wheel, as shown in the figure below. The radius ti the brakes is 20cm. The radius of the tire is 35cm.
To solve this problem, let's break it down step by step.
(a) Find the frictional force exerted by the road on each wheel:
First, let's calculate the vertical component of the force acting on each wheel. Since each wheel bears an equal part of the car's weight, the vertical force on each wheel is:
Vertical force = Weight of car / Total number of wheels
Vertical force = (1.07 x 10^4 N) / 4
Vertical force = 2.675 x 10^3 N
Now, let's calculate the frictional force using the formula:
Frictional force = Coefficient of friction * Normal force
Since the car is at rest and on an incline, the normal force acting on each wheel is equal to the vertical component of the force acting on each wheel, which we calculated earlier.
Now, we need to find the coefficient of friction. In the problem statement, the coefficient of friction was not given, so we can't calculate it directly. To proceed, we would need the coefficient of friction to solve for the frictional force.
(b) Find the sum of the magnitudes of the frictional forces fB applied by the brakes to the wheel:
To find the frictional force applied by the brakes to the wheel, we need to calculate the torque applied by the brakes.
Torque = Force * Distance
The force applied by the brakes is the frictional force we are looking for, and the distance is the radius of the brakes (20 cm). The torque will be equal for all four wheels since the problem states that the force applied by the axles is equal for each wheel.
Now, we can calculate the torque applied by the brakes using the formula:
Torque = Force * Distance
Torque = (Frictional force) * (Radius of the brakes)
Since we don't currently know the frictional force, we can't calculate the torque applied by the brakes to each wheel. Therefore, we can't find the sum of the magnitudes of the frictional forces fB applied by the brakes to the wheel without knowing the coefficient of friction or having more information about the problem.
In summary, we can solve for the frictional force applied by the road on each wheel but cannot solve for the sum of the magnitudes of the frictional forces applied by the brakes without additional information.