Frictional Force on Brake shoe

[Jimkatz809]

Homework Statement

A hydraulic brake system is shown. The area of the piston in the master cylinder is
6.35 cm2, and the area of the piston in the brake cylinder is 1.72 cm2. The coefficient of
kinetic friction between the brake shoe and the wheel drum is 0.453. How large is the frictional force between the brake shoe and the wheel drum when a force
of 46 N is exerted on the pedal? Answer in units of N.

Homework Equations

The Attempt at a Solution

I can't even figure out where to start on this one. Noo equations or anything. Please Help Me start this one.

 

[anathema]

Thank you for your question. I am happy to assist you with solving this problem.

To begin, we can use the equation F = μN, where F is the frictional force, μ is the coefficient of kinetic friction, and N is the normal force between the two surfaces. In this case, the two surfaces are the brake shoe and the wheel drum.

We are given the coefficient of kinetic friction as 0.453. To find the normal force, we can use the equation N = P/A, where P is the applied force and A is the area of the piston in the brake cylinder. Plugging in the given values, we get N = (46 N) / (1.72 cm^2) = 26.74 N.

Now, using the equation F = μN, we can calculate the frictional force between the brake shoe and the wheel drum. Plugging in the values, we get F = (0.453) (26.74 N) = 12.12 N.

Therefore, the frictional force between the brake shoe and the wheel drum when a force of 46 N is exerted on the pedal is 12.12 N.

I hope this helps you understand how to approach and solve this problem. Let me know if you have any further questions.


(Scientist)

 

[kerimek]

I would approach this problem by first understanding the concept of frictional force. Frictional force is the force that opposes the motion of an object when it comes into contact with another object. In this case, the brake shoe and the wheel drum are in contact with each other, and the frictional force between them is what helps to slow down or stop the rotation of the wheel.

To calculate the frictional force in this scenario, we can use the formula:

Frictional force = coefficient of kinetic friction * normal force

In this case, the normal force is the force exerted by the brake shoe on the wheel drum, which is equal to the force applied by the piston in the brake cylinder. We can calculate this force using the formula:

Force = pressure * area

In the master cylinder, the force exerted is equal to the force applied on the pedal, which is 46 N. Using the given areas of the pistons, we can calculate the pressure in the master cylinder as:

Pressure = Force / Area = 46 N / 6.35 cm^2 = 7.24 N/cm^2

Now, using the same formula, we can calculate the force exerted by the brake shoe on the wheel drum as:

Force = pressure * area = 7.24 N/cm^2 * 1.72 cm^2 = 12.45 N

Finally, we can calculate the frictional force using the first formula:

Frictional force = coefficient of kinetic friction * normal force = 0.453 * 12.45 N = 5.64 N

Therefore, the frictional force between the brake shoe and the wheel drum is 5.64 N when a force of 46 N is exerted on the pedal.