Final answer:
To raise a 3500-kg car using a hydraulic lift, a minimum force of 54880 N must be applied to the small piston with a cross-sectional area of 4.00 cm², based on Pascal's principle.
Step-by-step explanation:
The student has asked what minimum force must be applied to the small piston of a hydraulic lift in order to raise a 3500-kg car. This problem can be solved using Pascal's principle, which states that the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
First, we need to find the weight of the car, which is the force due to gravity acting on it. The weight (F2) can be calculated using the formula F2 = m × g, where m is the mass of the car (3500 kg) and g is the acceleration due to gravity (9.8 m/s2). This gives us a weight of 34300 N.
Using Pascal's principle, the relation between the forces and the areas of the pistons is expressed as:
F1/A1 = F2/A2
where:
- F1 is the force applied to the small piston
- A1 is the cross-sectional area of the small piston (4.00 cm2)
- A2 is the cross-sectional area of the large piston (2.50 cm2)
- F2 is the weight of the car (34300 N)
To find the required force F1, rearrange the equation to solve for F1:
F1 = F2 × (A1/A2)
Plugging in the known values gives us:
F1 = 34300 N × (4.00 cm2/2.50 cm2)
= 34300 N × 1.6
= 54880 N
This means that a minimum force of 54880 N must be applied to the small piston to raise the 3500-kg car.