A hydraulic brake system is shown. The
area of the piston in the master cylinder is 6.32 cm^2, and the area of the piston in the brake cylinder is 1.83 cm^2. The coefficient of kinetic friction between the brake shoe and the wheel drum is 0.443.
How large is the frictional force between the brake shoe and the wheel drum when a force of 49 N is exerted on the pedal? Answer in units of N.
Pascal’s principle F1/A1=F2/A2.
F(bc)={A(bc)/A(mc)}•F(pedal) =
=(1.83/6.32) •49 =14.2 N
This is the normal force exerted on the brake shoe.
The frictional force is
F(fr) =μ F(bc)=0.442•14.2 =6.3 N
Wow thank you so much! This problem has been bothering me for a week now
To determine the frictional force between the brake shoe and the wheel drum, we need to calculate the force exerted by the brake cylinder and then calculate the frictional force.
Step 1: Calculate the force exerted by the brake cylinder.
The force exerted by the brake cylinder can be determined using Pascal's law, which states that the pressure in a fluid is transmitted equally in all directions.
The formula to calculate the force exerted by the brake cylinder is:
Force in the brake cylinder = Force in the master cylinder * (Area of the brake cylinder / Area of the master cylinder)
Given:
Force in the master cylinder = 49 N
Area of the master cylinder = 6.32 cm^2
Area of the brake cylinder = 1.83 cm^2
Converting the areas from cm^2 to m^2:
Area of the master cylinder = 6.32 cm^2 * (1 m^2 / 10,000 cm^2) = 0.000632 m^2
Area of the brake cylinder = 1.83 cm^2 * (1 m^2 / 10,000 cm^2) = 0.000183 m^2
Calculating the force exerted by the brake cylinder:
Force in the brake cylinder = 49 N * (0.000183 m^2 / 0.000632 m^2) ≈ 14.237 N
Step 2: Calculate the frictional force.
The frictional force can be calculated using the formula:
Frictional force = Coefficient of kinetic friction * Normal force
Given:
Coefficient of kinetic friction = 0.443
The normal force can be calculated using Newton's second law, which states that the sum of the forces acting on an object equals the mass of the object times its acceleration, F = ma.
The normal force is equal to the force exerted by the brake cylinder.
Frictional force = 0.443 * 14.237 N ≈ 6.306 N
Therefore, the frictional force between the brake shoe and the wheel drum is approximately 6.306 N.