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Technology

Grade 9

Hydraulic and pneumatic systems

Module 11

Calculate the mechanical advantage of a hydraulic system

ACTIVITY 1:

To calculate the mechanical advantage of a hydraulic system

[LO 2.3]

An example of a simple hydraulic system is a hydraulic lift which is used to lift motor-cars. The system has a mechanical advantage of both power input and distance output.

The system consists of two pistons of different sizes, connected by a reservoir that is filled with a hydraulic liquid such as oil or water.

Mechanical advantage – force multiplication:

A smaller input force on the small piston results in a greater output force on the large piston so that there is a mechanical advantage.

The input force is called the effort and the output force is called the load.

The advantage is made possible by two characteristics of liquids, namely that they cannot be compressed and that they distribute pressure equally.

This principle is called Pascal’s principle.

The pressure at piston A is equal to the pressure at piston B.

Pressure is calculated as force per area.

Pressure cylinder A = Pressure cylinder B F orce A Area A = Force B Area B alignl { stack { size 12{"Pressure cylinder " size 11{`A=}"Pressure cylinder " size 11{`B}} {} #{ { size 11{F ital "orce"`A}} over { size 11{"Area"`A}} } = { { size 11{"Force"`B}} over { size 11{"Area"`B}} } {} } } {}

The following formula can be used to calculate the mechanical advantage:

Mechanical force advantage = load ( output force ) effort ( input force ) size 12{"Mechanical force advantage " size 11{ {}= { {"load " \( "output force" \) } over {"effort " \( "input force" \) } } }} {}

Mechanical advantage – distance output:

In the syringes the piston with the large diameter will have a smaller distance out­put, and the piston with the small diameter will have a larger distance output. The relationship of distance output is determined by the mechanical force advantage.

Example:

The motor-car in the above example weighs 5 000 N. The small piston, A, has an area of 1cm². The small piston moves across a distance of 100 cm.

(a) Determine the input force. According to Pascal’s principle:

Pressure cylinder A = Pressure cylinder B Force A Area A = Force B Area B Force A 1 = 5 000 N 100 Force A = 50 N alignl { stack { size 12{ size 11{"Pressure cylinder "`"A "="Pressure cylinder "`B}} {} #{} # { { size 11{"Force A"} } over { size 11{"Area A"} } } size 11{ {}= { {"Force B"} over {"Area B"} } } {} #{} # { { size 11{"Force A"} } over { size 11{1} } } size 11{ {}= { {"5 000 N"} over {"100"} } } {} #{} # size 11{"Force A "="50 N"} {}} } {}

The area at cylinder B is 100 times bigger. Therefore the power at cylinder A is 100 times smaller.

(b) Determine the mechanical force advantage.

MA = load effort = 5 000 50 = 100 alignl { stack { size 12{ size 11{"MA"= { {"load"} over {"effort"} } }} {} #{} # size 11{ {}= { {"5 000"} over {"50"} } } {} #{} # size 11{ {}="100"} {}} } {}

(c) Determine the distance that the large piston will move.

MA = 100. Therefore if the small piston moves 100 cm, the large piston will move 1 cm.

Test Your Knowledge

  1. A little boy receives a Jack-in-the-Box toy from his grandmother (see illustration).

1.1 Calculate the amount of force, in Newton, that the little boy needs to make the Jack-in-the-Box weighing 100 g shoot out, when the area at cylinder A is 2cm² and the area at cylinder B is 1cm².

1.2 Calculate the mechanical advantage in question 1.1

1.3 Calculate the distance that piston A must move to make the Jack-in-the-Box shoot out 3 cm.

1.4 Would it be more advantageous to change around the two pistons, A and B?

2. You have to make a pair of hydraulic pliers, as indicated in the sketch. To enable you to do this, you are given two cylinders with pistons of 2 cm and 1 cm respectively. The maximum distance that the larger piston can move in the cylinder is 3 cm. A force of 1N is applied to move the moving jaws of the pliers over a distance of 3 cm and to clamp the jaws of the pliers.

2.1 Which of the two pistons are you going to place in position A for a minimum force input? Explain your answer.

2.2 How far will the piston at cylinder A move to clamp the jaws?

Assessment

LO 2
TECHNOLOGICAL KNOWLEDGE AND UNDERSTANDINGThe learner will be able to understand and apply relevant technological knowledge ethically and responsibly.
We know this when the learner:
systems and control:2.3 demonstrates knowledge and understanding of interacting mechanical systems and sub-systems by practical analysis and represents them using systems diagrams:gear systemsbelt drive or pulley systems with more than one stage;mechanical control mechanisms (e.g. ratchet and pawl, cleats);pneumatic or hydraulic systems that use restrictorsone-way valves;systems where mechanical, electrical, or pneumatic or hydraulic systems are combined.

Memorandum

ACTIVITY 1

1.1 FORCE = 2 N

1.2 MA=1/2

1.3 1,5 cm

1.4 No, the small piston/plunger will move the furthest and enable Jack to make the highest jump

2.1 The piston/plunger with a diameter of 1 cm

2.2 1,5 cm

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
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Sherica
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Sherica
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Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Damian Reply
China
Cied
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abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Technology grade 9. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col11071/1.1
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