How Brakes Work 420... · How Brakes Work! Mark Lam University of British Columbia (Source:...

How Brakes Work!Mark LamUniversity of British Columbia

(Source: http://www.sub5zero.com/sites/default/files/uploads/2010/05/audi-r8-gt-01_0.jpg)

“Give me a place to stand on, and I will move the Earth.”

- Archimedes

(Source: http://www.math.nyu.edu/~crorres/Archimedes/Lever/Lever.jpg)

Mechanical AdvantageWhat are some situations where force must be amplified to carry out a task?


(Source: http://www.dimensionsinfo.com/wp-content/uploads/2010/01/Wheelbarrow.jpg)


(Source: http://www.mazda626.net/uploads/img-316189-1-Hydraulic-Floor-Jack.jpg)(Source: http://www.dimensionsinfo.com/wp-content/uploads/2010/01/Wheelbarrow.jpg)


(Source: http://www.mazda626.net/uploads/img-316189-1-Hydraulic-Floor-Jack.jpg)

(Source: http://www.vrajlinkchain.in/images/slide/3.jpg)(Source: http://www.dimensionsinfo.com/wp-content/uploads/2010/01/Wheelbarrow.jpg)


(Source: http://www.mazda626.net/uploads/img-316189-1-Hydraulic-Floor-Jack.jpg)

(Source: http://www.vrajlinkchain.in/images/slide/3.jpg)(Source: http://www.dimensionsinfo.com/wp-content/uploads/2010/01/Wheelbarrow.jpg)

(Source: http://static.ddmcdn.com/gif/wrench-1.jpg)

Mechanical Advantage


Mechanical advantage is a measure of the the force amplification of a system


Mechanical advantage is a measure of the the force amplification of a system

MA = Fout/Fin

Example

Using a pallet jack, I am able to raise 2000 lbs (~9000N) of goods with effort of 25N

What is the Mechanical Advantage of the Pallet Jack?

(Source: http://acestoragesolutions.com/yahoo_site_admin/assets/images/pallet_jack.202200555_std.jpg)

Example


Example

MA = Fout/Fin


Example

MA = Fout/FinFout = 9000 N


Example


Fin = 25 N


Example


Fin = 25 N

MA = 9000/25 = 360


Mechanical Advantage in Cars


We will discuss 2 ways in which force is amplified in order to stop a car:



1) Leverage (which you already may already be familiar with)



1) Leverage (which you already may already be familiar with)

2) Hydraulics (probably new to most of you)

LeverageArchimedes discovered that with the use of levers, one is able to amplify forces

The Law of the Lever can be expressed as

Findin = Foutdout

Leverage

Findin = Foutdout

Fout = Fin (din/dout)

MA = din/dout

Example - Scissors

(Source: http://www.fiskars.ca)

Example - Bolt Cutters

(Source: http://upload.wikimedia.org/wikipedia/commons/d/da/Bolt_cutters_animated.gif)

Leverage in Brakes

The brake pedal and the master cylinder are connected the same rod

When the force is applied to the brake pedal, that force is amplified and transmitted to the master cylinder.

(Source: http://www.cdxetextbook.com/images/350px-Brkpedalleverage.jpg)

Pressure

What is the difference between Force and Pressure?

Pressure

Pressure is the ratio of the Force to the Area over which the force is distributed

P = F/A (P is pressure, F = force, A = area)

Force tells you how an object will accelerate Pressure tells you how it will feel

(Source: http://www.youtube.com/watch?v=vo2iE94iAoA&feature=related)

ExampleWhich is greater: the force of Zdeno Chara standing with running shoes or Katy Perry standing with high heels?

(Source: http://en.wikipedia.org/wiki/File:Chara_cropped.jpg) (Source: http://www.zimbio.com/1950's+Hairstyles/articles/14)

ExampleWhich is greater: the pressure of Zdeno Chara standing with running shoes or Katy Perry standing with high heels?

(Source: http://en.wikipedia.org/wiki/File:Chara_cropped.jpg) (Source: http://www.zimbio.com/1950's+Hairstyles/articles/14)

Example

(Source: http://en.wikipedia.org/wiki/File:Chara_cropped.jpg)

Example

PChara = Fweight/Ashoes


Example

PChara = Fweight/Ashoesm = 115kg => Fweight = 1150N


Example


Ashoes = 2 x 500cm2 = 0.1m2


Example


Ashoes = 2 x 500cm2 = 0.1m2

PChara = 1150/0.1 = 11,500 Pa


Example

(Source: http://www.zimbio.com/1950's+Hairstyles/articles/14)

Example

PKaty = Fweight/Ashoes


Example

PKaty = Fweight/Ashoesm = 55kg => Fweight 550N


Example


Ashoes = 2 x 25cm2 = 0.005m2


Example


Ashoes = 2 x 25cm2 = 0.005m2

PKaty = 550/0.005 = 110,000 Pa


Example

PChara = 11,500 Pa

PKaty = 110,000 Pa

Who would you rather step on your foot?



Pressure in Liquids

We can also talk about pressure in liquids

In a body of water, the water pressure increases with depth because as you descend, the weight of water above you increases

(Source: http://en.wikipedia.org/wiki/Scuba_diving)

Pressure in Liquids

If we have a container with a piston on one end, we can apply pressure in the liquid by exerting a force on the piston

Pascal’s Principal

Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel.

What does this mean? How can we apply this?

Hydraulic SystemsHydraulic systems are made of 3 main parts:

an incompressible fluid

a container

pistons free to move at the ends of the container

(Source: http://auto.howstuffworks.com/auto-parts/brakes/brake-types/brake1.htm)

Example

Consider the system on the above. What do you expect to happen?

5kg 100kg

r=2m r=10m

(Source: http://www.linnbenton.edu/auto/brake/brake-fluid_valves_files/slide0002_image001.gif)

Hydraulic Systems


Hydraulic Systems

Pout = Pin


Hydraulic Systems

Pout = PinFout/Aout = Fin/Ain


Hydraulic Systems

Pout = PinFout/Aout = Fin/AinFout = Fin (Aout/Ain)


Hydraulic Systems

Pout = PinFout/Aout = Fin/AinFout = Fin (Aout/Ain)

MA = Aout/Ain


Example5kg 100kg

r=2m r=10m


ExampleMAhydraulics = Aout/Ain 5kg 100kg

r=2m r=10m



r=2m r=10mA=100π m2



r=2m r=10mA=4π m2 A=100π m2


ExampleMAhydraulics = Aout/AinMA = 100π/4π = 25

5kg 100kg

r=2m r=10mA=4π m2 A=100π m2



MA = Fout/Fin

5kg 100kg

r=2m r=10mA=4π m2 A=100π m2



MA = Fout/FinFout = MA x Fin

5kg 100kg

r=2m r=10mA=4π m2 A=100π m2



MA = Fout/FinFout = MA x Fin

5kg 100kg

r=2m r=10m

=>50N

A=4π m2 A=100π m2



MA = Fout/FinFout = MA x FinFout = 25 x 50 = 1250N

5kg 100kg

r=2m r=10m

=>50N

A=4π m2 A=100π m2




5kg 100kg

r=2m r=10m

=>50N =>1000N

A=4π m2 A=100π m2




1250N is enough to lift a mass of ~125kg.The 5kg mass will lower and the 100kg mass will rise

5kg 100kg

r=2m r=10m

=>50N =>1000N

A=4π m2 A=100π m2


Hydraulic Systems

(Source: http://science.howstuffworks.com/transport/engines-equipment/hydraulic1.htm)

Hydraulic SystemsIn hydraulic systems, there is often a trade-off of distance for force



To the right, the area of the input piston is 1π in2 and the area of the output piston is 9π in2 (9x larger)



To the right, the area of the input piston is 1π in2 and the area of the output piston is 9π in2 (9x larger)

Since the fluid is incompressible, the input piston must move 9 in for the output piston to move 1 in


Hydraulic Systems

(Source: http://www.jbgrimes.myclassupdates.com/sitebuildercontent/sitebuilderpictures/10068_nfg033.jpg)

Hydraulic Systems

Knowing this, we are able to lift heavy objects like cars


Hydraulic Systems

Knowing this, we are able to lift heavy objects like cars

Not only can we lift cars - we are able to stop cars as well


Hydraulics in Brakes

Hydraulics in BrakesWhen the brake pedal is pressed, the amplified force is transmitted to the master cylinder


The master cylinder then translates this force into hydraulic fluid pressure.



The pressure is transmitted to the slave pistons which come out to apply the brake pads on the rotor of each wheel



The pressure is transmitted to the slave pistons which come out to apply the brake pads on the rotor of each wheel

By friction, the kinetic energy is transformed into thermal energy as the car slows down

Hydraulic Braking System

(Source: http://www.chegg.com)

The Caliper

(Source: http://auto.howstuffworks.com/auto-parts/brakes/brake-parts/brake-calipers4.htm)(Source: http://auto.howstuffworks.com/auto-parts/brakes/brake-parts/brake-pads.htm)

Example

ExampleConsider a the following braking system:

The distance from the brake pedal to the pivot is 12 inches

The distance from the master cylinder to the pivot is 2 inches

The master cylinder has a radius of 1 inch

The master cylinder is connected to 8 slave cylinders (2 per wheel)

Each slave cylinder has a radius of 2 inches







What is the mechanical advantage of this system?








If I apply 100N of force on the brake pedal, what is the total force applied to the rotors?

Example

Example

MAlever = dpedal/dmaster cylinder

Example

MAlever = dpedal/dmaster cylinder = 12/2

Example

MAlever = dpedal/dmaster cylinder = 12/2 = 6

Example

MAlever = dpedal/dmaster cylinderMAhydraulics = Aslave cylinders/Amaster cylinder

= 12/2 = 6

Example


= 12/2 = 6

= 8 x 22π/12π

Example


= 12/2 = 6

= 8 x 22π/12π = 32

Example

MAlever = dpedal/dmaster cylinderMAhydraulics = Aslave cylinders/Amaster cylinderMAtotal = MAlever x MAhydraulics

= 12/2 = 6

= 8 x 22π/12π = 32

Example


= 12/2 = 6

= 8 x 22π/12π = 32

= 6 x 32

Example


= 12/2 = 6

= 8 x 22π/12π = 32

= 6 x 32 = 192

Example


MA = Fout/Fin

= 12/2 = 6

= 8 x 22π/12π = 32

= 6 x 32 = 192

Example


MA = Fout/FinFtotal = MAtotal x Fbrake pedal

= 12/2 = 6

= 8 x 22π/12π = 32

= 6 x 32 = 192

Example



= 12/2 = 6

= 8 x 22π/12π = 32

= 6 x 32 = 192

= 192 x 100

Example



= 12/2 = 6

= 8 x 22π/12π = 32

= 6 x 32 = 192

= 192 x 100 = 19,200 N

Example



Enough force to lift the car!

= 12/2 = 6

= 8 x 22π/12π = 32

= 6 x 32 = 192

= 192 x 100 = 19,200 N

Demonstration

Demonstration


MA = Aslave cylinders/Amaster cylinder

Demonstration


MA = Aslave cylinders/Amaster cylinderMA = (2 x Asyringe)/Asyringe

Demonstration


MA = Aslave cylinders/Amaster cylinderMA = (2 x Asyringe)/AsyringeMA= 2

Demonstration


MA = Aslave cylinders/Amaster cylinderMA = (2 x Asyringe)/AsyringeMA= 2

What changes could be made to make this fit to stop a car?

Summary

Summary

Mechanical Advantage is a measure of the force amplification of a system

Summary


Brakes combine 2 forms of mechanical advantage to multiply the force applied by your foot:

Summary



Leverage

Summary



Leverage

Hydraulics

Summary



Leverage

Hydraulics

With these, we can multiply our force over 200x

Leaks

(Source: http://auto.howstuffworks.com/auto-parts/brakes/brake-types/master-brake1.htm)

Power Brakes

(Source: http://auto.howstuffworks.com/auto-parts/brakes/brake-types/power-brake1.htm)

Anti-Lock Brakes (ABS)Skidding wheels have less traction than non-skidding wheels

This means that you have more control of your vehicle when braking if your wheels are still rotating

To keep your wheels from locking up, pressure is released when necessary

The result is a pulsing that keeps the wheel rotating as the car is moving

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How Brakes Work 420... · How Brakes Work! Mark Lam University of British Columbia (Source:...

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