Final answer:
A force of 36750 N must be applied by the large piston of a hydraulic lift to lift a 1500 kg vehicle, determined by the hydraulic principles that relate force to area while considering the weight of the vehicle and the areas of the pistons.
Step-by-step explanation:
To determine the force that must be applied by the large piston to lift a 1500 kg vehicle using a hydraulic lift, we first need to calculate the weight of the vehicle.
The weight can be found by multiplying the mass of the vehicle by the acceleration due to gravity (approximately 9.8 m/s2). For a 1500 kg vehicle, this would be 1500 kg × 9.8 m/s2 = 14700 N (Newtons).
In a hydraulic system, the pressure exerted on the small piston is transmitted equally to the large piston. The pressure (P) is defined as the force (F) applied per unit area (A), thus P = F/A.
Since the pressure is uniform across the system, we have Psmall = Plarge or (Fsmall/Asmall) = (Flarge/Alarge), where Fsmall is the force needed to lift the vehicle and Asmall is the area of the small piston, while Flarge is the unknown force we are solving for and Alarge is the area of the large piston.
Using the given areas, the equation becomes (14700 N/1 m2) = (Flarge/2.5 m2). Solving for Flarge, we find that Flarge = 14700 N × 2.5 m2 = 36750 N. Therefore, a force of 36750 N must be applied by the large piston to lift the 1500 kg vehicle.