A 13,000-N vehicle is to be lifted by a 25-cm diameter hydraulic piston.What force needs to be applied to a 5.0 cm diameter piston to accomplish this? Assume the pistons each have negligible weight.
A)260 N
B)520 N
C)2600 N
D)5200 N

Question

Quizplus · Accepted Answer

We can use the formula F1/A1 = F2/A2, where F1 is the force applied on the larger piston, A1 is its area, F2 is the force applied on the smaller piston, and A2 is its area. Rearranging to solve for F2, we get:
F2 = (F1/A1) × A2
Plugging in the given values:
F1 = 13,000 N
A1 = π(0.25 m)² = 0.049 m²
A2 = π(0.05 m)² = 0.0079 m²
F2 = (13,000 N / 0.049 m²) × 0.0079 m² = 520 N
Therefore, the force needed to lift the vehicle using the smaller piston is 520 N, which corresponds to choice B.

A 13,000-N Vehicle Is to Be Lifted by a 25-Cm