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.
To find the frictional force between the brake shoe and the wheel drum, we can use the equation:
frictional force = force applied * coefficient of friction
The force applied is 49 N and the coefficient of friction is 0.443.
So, the frictional force between the brake shoe and the wheel drum is:
frictional force = 49 N * 0.443 = 21.607 N
Therefore, the frictional force between the brake shoe and the wheel drum when a force of 49 N is exerted on the pedal is 21.607 N.
To find the frictional force between the brake shoe and the wheel drum, we need to consider the hydraulic brake system.
First, let's find the force exerted by the master cylinder on the brake cylinder using Pascal's law - the pressure is transmitted equally in all directions in an enclosed fluid. The formula for pressure is:
Pressure = Force / Area
Since the area of the piston in the master cylinder is 6.32 cm^2 and a force of 49 N is exerted on the pedal, we can find the pressure exerted on the hydraulic fluid:
Pressure = 49 N / 6.32 cm^2
To calculate this, you need to convert the area to square meters: 6.32 cm^2 = 6.32 * 10^(-4) m^2.
Pressure = 49 N / 6.32 * 10^(-4) m^2
Next, we can use this pressure to find the force exerted by the hydraulic fluid on the brake cylinder. Since the pressure is transmitted equally to all parts of the fluid, the force applied by the brake cylinder is equal to the pressure multiplied by the area of the piston in the brake cylinder:
Force brake cylinder = Pressure * Area brake cylinder
Given that the area of the piston in the brake cylinder is 1.83 cm^2, we need to convert it to square meters: 1.83 cm^2 = 1.83 * 10^(-4) m^2.
Force brake cylinder = Pressure * 1.83 * 10^(-4) m^2
Now that we have the force exerted by the brake cylinder, we can calculate the frictional force between the brake shoe and the wheel drum. The formula to calculate frictional force is:
Frictional force = coeff_fric * Force brake cylinder
Given that the coefficient of kinetic friction between the brake shoe and the wheel drum is 0.443, we can use this value in the equation:
Frictional force = 0.443 * Force brake cylinder
Substituting the value of the force exerted by the brake cylinder into the equation, we get:
Frictional force = 0.443 * (Pressure * 1.83 * 10^(-4) m^2)
Now you can plug in the calculated values to get the final answer in units of Newtons (N).