Question

Hydraulic systems utilize Pascal's principle by transmitting pressure from one cylinder (called the primary) to another (called the secondary). Since the pressures will be equal, if the surface areas are different then the forces applied to the cylinders' pistons will be different. Suppose in a hydraulic lift, the piston of the primary cylinder has a 2.1-cm diameter and the piston of the secondary cylinder has a 26-cm diameter.
What force, in newtons, must be exerted on the primary cylinder of this lift to support the weight of a 2200-kg car (a large car) resting on the secondary cylinder?

Answer 1

Answer:

The force to be applied on the primary piston is 140.63 N.

Explanation:

To solve this problem we apply the following formulas:

Pascal principle: F=P*A   Formula (1)

F=Force applied to the piston

P: Pressure

A= Piston area

$A=\frac{\pi*d^{2} }{4}$ Formula (2)

d= piston diameter

Nomenclature:

Fp= Force on the primary piston

Fs= Force on the secondary piston

Ap= Primary piston area

As= Secondary piston area

W= car weight

Calculation of the force Fp necessary to support the weight of the car.

Pascal principle: Fp=P*Ap (Equation1)

In (Equation1) we know Ap and we don't know P.

Pressure calculation:

We apply Newton's first law for a balanced Secondary piston -automobile system

Newton's first law: ∑F=0

W-Fs=0

W=Fs

W=P*As

$P=\frac{W}{As}$

We replace $P=\frac{W}{As}$in equation 1:

$Fp=\frac{W}{As} *Ap$

$Fp=\frac{W}{\frac{\pi*d_{s}^{2} }{4} } *\pi *\frac{d_{p^{2} } }{4}$

$Fp=W*\frac{d_{p}^{2} }{d_{s}^{2} }$

$Fp=2200*\frac{2,1^{2} }{26^{2} }$

$Fp=2200*\frac{4.41}{676}$

$Fp=14.35kg$

Calculation of Fp in Newtons (N):

$1kg=9.8N$

$Fp=14.35kg*\frac{9.8N}{kg}$

Fp=140.63N