A 12,000-N car is raised using a hydraulic lift,which consists of a U-tube with arms of unequal areas,filled with incompressible oil and capped at both ends with tight-fitting pistons.The wider arm of the U-tube has a radius of and the narrower arm has a radius of .The car rests on the piston on the wider arm of the U-tube.The pistons are initially at the same level.What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem,you can neglect the weight of the pistons.)
A) 727 N
B) 926 N
C) 2900 N
D) 3330 N
E) 1.20 kN

Question

A 12,000-N car is raised using a hydraulic lift,which consists of a U-tube with arms of unequal areas,filled with incompressible oil and capped at both ends with tight-fitting pistons.The wider arm of the U-tube has a radius of  and the narrower arm has a radius of  .The car rests on the piston on the wider arm of the U-tube.The pistons are initially at the same level.What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem,you can neglect the weight of the pistons.)
A) 727 N 
B) 926 N 
C) 2900 N 
D) 3330 N 
E) 1.20 kN

Quizplus · Accepted Answer

The hydraulic lift works using Pascal's principle, which states that pressure applied to a fluid is transmitted equally throughout the fluid in all directions. Therefore, the pressure on the smaller piston is equal to the pressure on the larger piston.

We can use the formula for pressure, which is P = F/A, where P is pressure, F is force, and A is area. We can set the pressure on the smaller piston equal to the pressure on the larger piston:

F small / A small = F car / A car

We can solve for F small :

F small = F car (A small / A car)

The area of the larger piston is:

A car = πr2 = π(11.83 m)2 = 441.16 m2

The area of the smaller piston is:

A small = πr2 = π(1.83 m)2 = 10.52 m2

The force required to lift the car (F car ) is 12,000 N.

Plugging in the values, we get:

F small = 12,000 N (10.52 m2 / 441.16 m2) ≈ 285.7 N

Therefore, the initial force required to start lifting the car is approximately 286 N, which is closest to option B (926 N).

A 12,000-N Car Is Raised Using a Hydraulic Lift,which Consists