Answer:
9800 N.
Step-by-step explanation:
To calculate the weight of the car using the hydraulic system, we first find the force exerted by the master cylinder and then determine the total force exerted by all four slave cylinders combined.
Force exerted by the master cylinder:
The force exerted by the master cylinder can be calculated using the formula:
Force (master) = Pressure (master) × Area (master)
Given data:
Gravity force = 9.8 N/kg
Weight of the car = 1000 kg
Cross-sectional area of the master cylinder piston = 0.00125 m^2
Force (master) = Gravity force × Weight of the car
Force (master) = 9.8 N/kg × 1000 kg
Force (master) = 9800 N
Total force exerted by all slave cylinders combined:
Since the force is transmitted evenly to all slave cylinders, the force exerted by each slave cylinder is the same as the force exerted by the master cylinder.
Total Force (slave) = Force (master) × Number of Slave Cylinders
Total Force (slave) = 9800 N × 4
Total Force (slave) = 39200 N
The weight of the car:
The total force exerted by all slave cylinders combined is equal to the weight of the car.
Weight of the car = Total Force (slave)
Weight of the car = 39200 N
Therefore, the weight of the car is 39200 N, which is equivalent to approximately 9800 kg (since 1 N = 0.102 kg due to Earth's gravity force).