A car's brake system transfers pressure from the main cylinder to the brake shoes on all four wheels. The surface area of the main cylinder piston is 7.2 sq cm, and that of the piston in each individual brake cylinder is 1.80 sq cm. The driver exerts a 5.00 N force on the pedal. What is the pressure added to the liquid in the brake system? And the force exerted on each broke shoe?
The driver pushes the pedal moving the piston 2 cm in the main cylinder. How much does the piston move in each of the brake cylinders?
To find the pressure added to the liquid in the brake system, we can use the formula:
Pressure = Force / Area
First, let's calculate the pressure added to the liquid in the brake system:
1. Calculate the area of the main cylinder piston:
Area of the main cylinder piston = 7.2 sq cm
2. Now, calculate the pressure added to the liquid in the brake system:
Pressure = Force / Area of the main cylinder piston
Pressure = 5.00 N / 7.2 sq cm
Pressure ≈ 0.69 N/cm² (rounded to two decimal places)
Therefore, the pressure added to the liquid in the brake system is approximately 0.69 N/cm².
Next, let's calculate the force exerted on each brake shoe:
1. Calculate the area of the piston in each individual brake cylinder:
Area of each brake cylinder piston = 1.80 sq cm
2. Since the pressure is the same throughout the brake system, the force exerted on each brake shoe can be calculated using the formula:
Force = Pressure x Area of each brake cylinder piston
Force = 0.69 N/cm² x 1.80 sq cm
Force ≈ 1.24 N (rounded to two decimal places)
Therefore, the force exerted on each brake shoe is approximately 1.24 N.
Now, let's determine how much the piston moves in each of the brake cylinders:
The piston in the main cylinder moves 2 cm. Since the pressure is constant throughout the brake system, the movement of the piston in each brake cylinder will be the same.
Therefore, the piston in each of the brake cylinders also moves 2 cm.