3.4 APPLYING PASCAL’S PRINCIPLE

Learning Outcome:State Pascal’s PrincipleExplain hydraulic systemDescribe applications of Pascal’s principleSolve problems involving Pascal’s principle

INTRODUCTION

Diagrams show an excavators digging up soil .

How can the huge and heavy parts move easily ?

It is a very big and heavy machine.

Transmission of pressure

When the icing sugar is pressed, pressure is transmitted.

How to get the toothpaste flowing out of its mouth ?

What happen if the tube of tooth paste has various leaks ?

Explain why toothpaste also flow out from these leaks.

Transmission of liquid pressure

Water spurts out from the plunger in all directions .

Water spurts out to the same distance away.

Hands-on activity :

1.Press the piston.

2.Observe the directions in which the water squirts out.

3.Observe the strength of the squirting water.

Transmission of pressure in a liquid

states that pressure applied to an enclosed liquid is transmitted uniformly in all directions.

Pascal ‘s principle

Hands – on activity 3.5 pg 59 of practical book

Hydraulic System

Based on Pascal’s Principle,

1 2

1 2

F F

A A

P1 = P2

Therefore,

P1 = Pressure on small piston

P2= Pressure on big piston

F1 = input force , A1 = small piston area

F2 = output force , A2 = big piston area

Output force

22 1

1

AF x F

A

is a force multiplier

Multiplying factor

Application of Pascal’s Principle

in out

in out

F F

A A

outout in

in

AF x F

A

1. Hydraulic lift

in out

in out

F F

A A hence

Aout is much bigger than Ain

A heavy object like a car is able to be lifted by a much smaller input force.

P1= P2

Application of Pascal’s Principle

•The driver’s foot presses the brake pedal.

•The piston in the master cylinder exerts pressure on the brake fluid.

•This pressure is transmitted to the wheel cylinder of all wheels.

•The pressure causes the pistons to press the brake shoes against

the wheels to slow down the car.

Why the piston of the wheel cylinder is

larger than that of the master cylinder ?

2. Hydraulic brakes

What is the function of the return spring ?

Worked example pg 95

In a hydraulic brake, a force of 60 N is applied to a piston with area of 3 cm2.

(a) What is the pressure transmitted throughout the liquid ?

(b) If the piston at the wheel cylinder has an area of 8 cm2, what is the force exerted on it ?

solution

(a) PrForce

essureArea

= 60 N 3 cm2

= 20 N cm-2

(b) Force = Pressure x Area

= 20 N cm-2 x 8 cm2

= 160 N

Worked example (Exploring pg 182)

A basic hydraulic system has small and large pistons with cross-sectional areas of 2 cm2 and 50 cm2 respectively. When a force of 20 N is applied to the small piston, it pushes down the piston by 20 cm. Calculate

(a) The pressure , transmitted in the hydraulic fluid,(b) The force acting on the large piston,(c) the distance moved by the large piston, and(d) the magnification of the force.

(a) PrForce

essureArea

2

20

2

N

cm

= 10 N cm-2

solution

Worked example (Exploring pg 182)

A basic hydraulic system has small and large pistons with cross-sectional areas of 2 cm2 and 50 cm2 respectively. When a force of 20 N is applied to the small piston, it pushes down the piston by 20 cm. Calculate

(a) The pressure ,in Pa, transmitted in the hydraulic fluid,(b) The force acting on the large piston,(c) the distance moved by the large piston, and(d) the magnification of the force.

solution

100 000 Pa

(b) Force = pressure x area

F2 = P2 x A2

F2 = 10 N cm-2 x 50 cm2

= 500N

Worked example (Exploring pg 182)

A basic hydraulic system has small and large pistons with cross-sectional areas of 2 cm2 and 50 cm2 respectively. When a force of 20 N is applied to the small piston, it pushes down the piston by 20 cm. Calculate

(a) The pressure ,in Pa, transmitted in the hydraulic fluid,(b) The force acting on the large piston,(c) the distance moved by the large piston, and(d) the magnification of the force.

solution

100 000 Pa

(c) Volume of liquid transferred is constant

2 x 20 = h x 50

500 N

h = 0.8 cm

Worked example (Exploring pg 182)

A basic hydraulic system has small and large pistons with cross-sectional areas of 2 cm2 and 50 cm2 respectively. When a force of 20 N is applied to the small piston, it pushes down the piston by 20 cm. Calculate

(a) The pressure ,in Pa, transmitted in the hydraulic fluid,(b) The force acting on the large piston,(c) the distance moved by the large piston, and(d) the magnification of the force.

solution

100 000 Pa

(c) Magnification of force

= F2 / F1

500 N

= 500 20

0.8 cm

or A2 /A1

= 25 time

EVALUATION

1. Which of the following is an application of Pascal’s principle.

A Syringe

B Car brakes

C Wide tractor’s tyre

D Public water supply system

EVALUATION

2. Diagram show a hydraulic lift.

Which of the following gives the correct relationship ?

symbol relationship

P F1 = F2

Q F1< F2

R F1 F2

A1 A2

S F1 F2

A1 A2

<

=

A P,R B P,S C Q,R D Q,S

EVALUATION

A 300 N

B 420 N

C 500 N

D 525 N

E 675 N

EVALUATION

A

B

C

D

Home work

Mastery Practice 3.4 pg 95

Challenge Yourself pg 96

Check your progress 3.4 Exploring pg 183