Answer :
Final answer:
To lift a car weighing 3700 N on a hydraulic lift using a smaller piston of 0.072 m², Pascal's Principle is applied, but the calculated force does not match the provided answer options (a-d). (Option D).
Explanation:
The calculate the force that must be applied to a smaller piston in a hydraulic lift in order to lift a car. This problem is based on Pascal's Principle which states that pressure exerted anywhere in a confined fluid is transmitted equally in all directions throughout the fluid such that the pressure variations remain the same. The formula derived from Pascal's Principle for a hydraulic system is:
F1/A1 = F2/A2
Where F1 is the force applied on the smaller piston, A1 is the area of the smaller piston, F2 is the force exerted by the larger piston (which is the weight of the car), and A2 is the area of the larger piston.
Given F2 = 3700 N (weight of the car) and A2 = 2.8 m2 (area of the platform on which the car is placed), we can rearrange the formula to solve for F1, the force exerted on the smaller piston:
F1 = (F2 × A1) / A2
Since we are given the area of the smaller piston (A1 = 0.072 m2), we can now calculate F1:
F1 = (3700 N × 0.072 m2) / 2.8 m2
F1 = 95.04 N
However, this result does not match any of the provided options (a-d), which suggests there may be an error in the information provided in the question or in the answer options. If the available options do not have the correct answer, it would be best to communicate this discrepancy to the student. (Option D).
