Final answer:
To lift a car using a hydraulic lift with a radius of 5.0 cm for the small piston and 15 cm for the large piston, Pascal's principle can be used to calculate the force required.
The weight of the car is the starting point, and from there, the force on the smaller piston is derived using the area ratio.
Step-by-step explanation:
The student has asked to calculate the force required on a small piston to lift a car using a hydraulic system, in accordance with Pascal's principle.
First, it is necessary to determine the weight of the car, which is the product of its mass and the acceleration due to gravity (F2 = mass × g). The car's weight is then 1350 kg × 9.8 m/s2, which equals 13230 N.
Pascal's principle states that the pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls of its container.
Therefore, the force exerted on the small piston (F1) is related to the force on the larger piston (F2) and their respective areas (A1 and A2).
Using the formula F1 = (A1 / A2) × F2, where A1 = π × (radius of small piston)2 and A2 = π × (radius of large piston)2, we can calculate the necessary force.
With A1 being π × (5 cm)2 and A2 being π × (15 cm)2, the force F1 can be determined. It is important to remember to convert the radii from centimeters to meters when calculating areas in SI units, as the force must be in newtons.