Force in Mechanical Force in Mechanical SystemsSystems

Measuring

Measuring

There are several systems of measurement. English Cgs (very small) Avoirdupois (ballistics) SI (metric)

We will be using English and metric (SI)

Measuring Length with a ruler

For length we use a ruler for lengths under a foot or a tape measure for longer lengths.

Tape Measure

Once you can read a ruler you certainly can use a tape measure which is used in many different careers and activities.

View the link on using a tape measure

Play the ruler game

Measuring lengths with a caliper or micrometer

For smaller lengths we use vernier calipers or very small lengths (thicknesses) we use a micrometer

Metric (SI) SystemMetric (SI) System

Force in Mechanical SystemForce in Mechanical System How do we measure forces?How do we measure forces?

The English unit for force is the The English unit for force is the

pound (lb.)pound (lb.)

The metric unit for force is the The metric unit for force is the Newton (N) Newton (N)

A NewtonA Newton

1 Newton is approximately 1 stick of 1 Newton is approximately 1 stick of margarine or butter (1/4 pound)margarine or butter (1/4 pound)

KKinging HHenryenry DDoesn’toesn’t MMindind DDiscussingiscussing CChurchhurch MMattersatters

International System (SI)International System (SI)

root units : meter liter gramroot units : meter liter gram Base UnitsBase Units Base units are meter, kilogram, second,…Base units are meter, kilogram, second,… (see table 2 on page 6)(see table 2 on page 6)

Kilo hecto Deka (root) deci centi milliKilo hecto Deka (root) deci centi milli K H Da d c mK H Da d c m

1000 100 10 1 0.1 0.01 0.0011000 100 10 1 0.1 0.01 0.001

101033 10 1022 10 1011 10 1000 10 10-1-1 10 10-2-2 10 10-3-3

Metric ActivityMetric Activity

You will need a meter stickYou will need a meter stick

Remember:Remember:-a millimeter is slightly less than a dime-a millimeter is slightly less than a dime-a centimeter is width of a pinky finger-a centimeter is width of a pinky finger-a decimeter is about a hand width-a decimeter is about a hand width-a meter is slightly longer than the -a meter is slightly longer than the distance from your nose to your finger tipsdistance from your nose to your finger tips

Changing Prefixes- 1Changing Prefixes- 1

Make a chartMake a chart

K / H / Da / meter, liter , gram / d / c / mK / H / Da / meter, liter , gram / d / c / m

378 cm to m378 cm to m

The decimal moves 2 places to the leftThe decimal moves 2 places to the left

3.78 m3.78 m

Changing Prefixes - 2Changing Prefixes - 2

Property of OneProperty of One

378 cm to m378 cm to m

100 cm = 1 m100 cm = 1 m

378 cm378 cm X X 1 m1 m = 3.78 m = 3.78 m 1 100 cm 1 100 cm

Force in Mechanical SystemForce in Mechanical SystemWhat are other common units?What are other common units?

SISI EnglishEnglishLengthLength meter (m) meter (m) foot (ft) foot (ft)Time Time second (s)second (s) second (s) second (s)Mass Mass kilogram Pound kilogram Pound

massmassWeight Weight Newton (N)Newton (N) Pound (lb) Pound (lb)

Mass & weight conversionsMass & weight conversions- 1 pound = 4.45 Newtons1 pound = 4.45 Newtons- 1 kilogram weighs 9.8 Newtons1 kilogram weighs 9.8 Newtons

AssignmentsAssignments

Measuring ActivitiesMeasuring Activities

Linear Math 1Linear Math 1

Mass vs WeightMass vs WeightWhat is the difference between weight What is the difference between weight

and mass?and mass?

--MassMass – the amount of matter in a – the amount of matter in a

objectobject

- measured in pound mass (lbm), - measured in pound mass (lbm),

grams or kggrams or kg

--Weight Weight – mass – mass andand the measure of the the measure of the

Earth’s gravitational pullEarth’s gravitational pull

- measured in pounds (lb) or - measured in pounds (lb) or newtonsnewtons

Force in Mechanical SystemForce in Mechanical SystemCan mass change?Can mass change?

- no, mass does not - no, mass does not changechange

Can weight change?Can weight change?

-yes, weight can change -yes, weight can change as gravity changesas gravity changes

Gravity is 1/6 less on the Gravity is 1/6 less on the moon.moon.

Weight is a forceWeight is a force

Weight is a force caused by the Weight is a force caused by the Earth’s gravityEarth’s gravity

GravityGravity

Varies with elevationVaries with elevation Mt Everest Mt Everest

– – weigh lessweigh less Death Valley Death Valley

– – weigh moreweigh more

Would you weigh more or less in New Would you weigh more or less in New Orleans? Orleans?

More you are below sea levelMore you are below sea level

Force in Mechanical SystemForce in Mechanical System

Are mass and weight the same Are mass and weight the same thing?thing?

- no, mass and weight are very - no, mass and weight are very differentdifferent

You weigh 120 lbs on Earth. What You weigh 120 lbs on Earth. What do you weigh on the moon?do you weigh on the moon?

20 lbs 20 lbs

In SpaceIn Space

Your spine lengthens by 2 inches Your spine lengthens by 2 inches when in 0 gravity.when in 0 gravity.

Weight = mass X GravityWeight = mass X Gravity

VariableVariable EnglishEnglish SISI

WeightWeight W W lblb NN

MassMass m m lb-masslb-mass kgkg

GravityGravity g g 32 ft/s32 ft/s22 9.81 m/s9.81 m/s22

To convert mass to weightTo convert mass to weight

In our labs we convert mass/weight in SIIn our labs we convert mass/weight in SI

EX: Use the Property of OneEX: Use the Property of One

500 g X 500 g X 0.00981 N0.00981 N = 4.905 N = 4.905 N 1 g1 g

100 Kg X 100 Kg X 9.81 N9.81 N = 981 N = 981 N 1 Kg1 Kg

Convert Weight to massConvert Weight to mass

EX: Use the Property of OneEX: Use the Property of One

25 N X 25 N X 1 kg1 kg = 2.55 Kg = 2.55 Kg

9.81 N9.81 N

4 N X 4 N X 1 g1 g = 407.7 g = 407.7 g

0.00981 N0.00981 N

Weight and mass math wsWeight and mass math ws

Vectors and SystemsVectors and Systems

What two factors determine the What two factors determine the effect of a force?effect of a force?

- the strength of the force- the strength of the force

- direction of the force- direction of the force

What is the strength of the force What is the strength of the force called?called?

- Magnitude- Magnitude

Force in Mechanical SystemForce in Mechanical System

What is the difference between What is the difference between vectors and scalars?vectors and scalars?- a vector is a physical quantity - a vector is a physical quantity that has both a magnitude and that has both a magnitude and directiondirection

- forces, velocity, acceleration- forces, velocity, acceleration- a scalar quantity only has a - a scalar quantity only has a magnitudemagnitude

- - temperature, pressure, masstemperature, pressure, mass

Force in Mechanical SystemForce in Mechanical System

What is the difference between What is the difference between vectors and scalars?vectors and scalars?- a vector is a physical quantity - a vector is a physical quantity that has both a magnitude and that has both a magnitude and directiondirection

- forces, velocity, acceleration- forces, velocity, acceleration- a scalar quantity only has a - a scalar quantity only has a magnitudemagnitude

- - temperature, pressure, masstemperature, pressure, mass

Which are vectors????Which are vectors????

55 mph 55 mph 55mph, E55mph, E

20 ft, left20 ft, left 20 ft20 ft

30 N at 20 degrees 30 N at 20 degrees 30 N30 N

5 mm5 mm 5 mm, down5 mm, down

AnswersAnswers to Vectors to Vectors

Any number with a directionAny number with a direction 55 mph 55 mph 55mph, E55mph, E

20 ft, left20 ft, left 20 ft20 ft

30 N at 20 degrees30 N at 20 degrees 30 N*30 N*

5 mm5 mm 5 mm, down5 mm, down *Sometimes the unit indicates direction*Sometimes the unit indicates direction

How can we represent forces?How can we represent forces?

- all vectors can be represented by - all vectors can be represented by arrowsarrows

- the arrow length represents - the arrow length represents the the magnitude of the forcemagnitude of the force

- the arrow heading represents - the arrow heading represents the the direction of the forcedirection of the force

TailTail Head Head

Force in Mechanical SystemForce in Mechanical System

Consider the example – A worker Consider the example – A worker pulls a heavy cart with a force of pulls a heavy cart with a force of 30 pounds at an angle of 3030 pounds at an angle of 30oo above the floor. Draw out this above the floor. Draw out this vector.vector.

30 lbs

30o

What is a balanced What is a balanced force?force?

- forces that are equal in size forces that are equal in size and opposite in directionand opposite in direction

- THERE IS NO MOVEMENTTHERE IS NO MOVEMENT

example: two men example: two men pushing on a fencepushing on a fence

What is an unbalanced force?What is an unbalanced force?

- force that unequal in either size - force that unequal in either size or directionor direction

- - causes movementcauses movement

example – man pushing lawn example – man pushing lawn mower, the mower movesmower, the mower moves

What is a net force?What is a net force?

- the force that is leftover when all - the force that is leftover when all forces are taken into considerationforces are taken into consideration

A man pulls a rope with 5 N of force A man pulls a rope with 5 N of force to the right. A second man pulls to the right. A second man pulls with 15 N of force to the left. What with 15 N of force to the left. What is the net force on the rope?is the net force on the rope?

- - 10 N to the left10 N to the left

Are the forces on the rope Are the forces on the rope balanced or unbalanced?balanced or unbalanced?

- unbalanced- unbalanced

Will the rope move?Will the rope move?

- Yes, because an unbalanced - Yes, because an unbalanced force causes motionforce causes motion

Example – Four people are playing tug of Example – Four people are playing tug of war. Two people on one side pull against war. Two people on one side pull against two people on the other side. The two on two people on the other side. The two on the right each pull with 50 pounds of force. the right each pull with 50 pounds of force. The two on the left pull with 70 pounds of The two on the left pull with 70 pounds of force. What is the net force? (magnitude force. What is the net force? (magnitude

and direction)and direction)

40 pounds of force to the right 40 pounds of force to the right (net force)(net force)

Newton’s LawsNewton’s Laws

When is a body at equilibrium?When is a body at equilibrium? -- when all forces are when all forces are

equalequal

- the body is at rest- the body is at rest

What will happened to a body if it is What will happened to a body if it is at rest and balanced force are at rest and balanced force are applied to it?applied to it?- it will stay at rest (Newton’s First - it will stay at rest (Newton’s First Law of Motion)Law of Motion)

Newton’s 1Newton’s 1stst Law of Motion Law of Motion(also Law of Inertia)(also Law of Inertia)

An object at rest will remain at An object at rest will remain at restrest

An object in motion will remain in An object in motion will remain in motionmotion

Unless acted upon by an Unless acted upon by an unbalanced force.unbalanced force.

If a body is at rest and unbalanced forces If a body is at rest and unbalanced forces (net force) act on it, what will happen?(net force) act on it, what will happen?

- the body will be - the body will be accelerated in the accelerated in the direction of the direction of the force (Newton’s force (Newton’s Second Law of Second Law of Motion)Motion)

Newton’s 2Newton’s 2ndnd Law Law

F = m aF = m a

If you push down a trampoline with If you push down a trampoline with 10 N of force, what how much force 10 N of force, what how much force

will push back on you?will push back on you?

- 10 N of force will push - 10 N of force will push you upyou up

- Newton’s Third Law of - Newton’s Third Law of Motion – for every action, Motion – for every action, there is an equal and there is an equal and opposite reactionopposite reaction

Newton’s 3Newton’s 3rdrd Law of Motion Law of Motion

For every action For every action there is an equal there is an equal and opposite and opposite reactionreaction

Adding VectorsAdding Vectors

How do we add forces that act How do we add forces that act along the same line?along the same line?

- if the forces act in the same direction, - if the forces act in the same direction, we we addadd magnitude of the forces magnitude of the forces

- if the forces act in opposite - if the forces act in opposite directions, we directions, we subtractsubtract the the magnitude of the forcesmagnitude of the forces

Vector AdditionVector AdditionJoe’s car runs out of gas. Joe’s friend Joe’s car runs out of gas. Joe’s friend

Anne helps Joe push the car into the Anne helps Joe push the car into the gas station. Joe pushes with 200 lb gas station. Joe pushes with 200 lb and Anne pushes with 180 lb. What and Anne pushes with 180 lb. What is the net force?is the net force?

380 lb forward380 lb forward

What would happen if the two teams below What would happen if the two teams below both pulled with a force of 750 lb?both pulled with a force of 750 lb?

- the rope would not move because - the rope would not move because the forces are balanced or in the forces are balanced or in equilibriumequilibrium

Force in Mechanical SystemForce in Mechanical SystemHow do we add forces that act at an How do we add forces that act at an

angle?angle?

- you cannot add forces when they - you cannot add forces when they act at anglesact at angles

- you can solve them graphically- you can solve them graphically

What is the overall force when multiple What is the overall force when multiple forces are acting on an object?forces are acting on an object?

- a resultant force- a resultant force

- the resultant always acts in a - the resultant always acts in a direction between the directions of direction between the directions of the two forcesthe two forces

Graphical AnalysisGraphical Analysis

Vectors are drawn as accurate as Vectors are drawn as accurate as possible.possible.

Rulers and protractors are usedRulers and protractors are used

Used when you don’t use Used when you don’t use trigonometry trigonometry

Forces at AnglesForces at Angles- - Step OneStep One – Look at the force vectors – Look at the force vectors

- Choose scale for the line- Choose scale for the line-for ex: 1 cm = 10 lb -for ex: 1 cm = 10 lb - use a ruler- use a ruler

--Step Two-Step Two- Place a dot on the paper Place a dot on the paper

- Step ThreeStep Three –Draw the two force vectors –Draw the two force vectors coming out of the dot while using the coming out of the dot while using the scale, ruler and protractor (Be sure you are scale, ruler and protractor (Be sure you are drawing the vectors in the correct drawing the vectors in the correct direction)direction)

Force in Mechanical SystemForce in Mechanical System

--Step FourStep Four – Draw a parallelogram – Draw a parallelogramALWAYS add the tail of the second vector to the ALWAYS add the tail of the second vector to the

head of the first vectorhead of the first vector

-Step Five-Step Five – Draw the resultant force- (the – Draw the resultant force- (the diagonal line from the dot to the end diagonal line from the dot to the end corner)corner)

--Step SixStep Six – Measure the length of the – Measure the length of the resultant (magnitude) and measure the resultant (magnitude) and measure the angle on either side (direction)angle on either side (direction)

- - use the ruler and protractoruse the ruler and protractor

EX: Two people pull on a boat with EX: Two people pull on a boat with ropes that form a right angle. The ropes that form a right angle. The person on the right of the boat (on person on the right of the boat (on the dock) pulls with 40 pounds of the dock) pulls with 40 pounds of force. The person in front of the boat force. The person in front of the boat (on shore) pulls with 30 pounds of (on shore) pulls with 30 pounds of force. What is the resultant force of force. What is the resultant force of the boat?the boat?

Draw the 30 lb vector 3 inches long Draw the 30 lb vector 3 inches long and the 40 lb vector 4 inches long.and the 40 lb vector 4 inches long.

30 lb30 lb

40 lbs40 lbs

Measure the Net ForceMeasure the Net Force

Make a parallelogram and measure the net Make a parallelogram and measure the net force (resultant) which is the diagonal line.force (resultant) which is the diagonal line.

measure the angles on either side of the measure the angles on either side of the dotdot

30 lbs30 lbs

40 lbs40 lbs

AnswerAnswer

The resultant or net force is the path The resultant or net force is the path that the boat will takethat the boat will take

Net force = 50 lbs ( the line was 5 Net force = 50 lbs ( the line was 5 inches)inches)

Angles 53Angles 53oo, 37, 37oo

TorqueTorqueWhat is torque?What is torque?

- the effect of a force applied on - the effect of a force applied on a body at some distance from the axis a body at some distance from the axis of rotation of that bodyof rotation of that body

- torque causes rotation- torque causes rotation

What are two ways an object can rotate?What are two ways an object can rotate?

- clockwise and counterclockwise- clockwise and counterclockwise

TorqueTorque

When is torque used?When is torque used?

- opening a paint - opening a paint can, opening a door, can, opening a door, using a wrench to using a wrench to turn a nut, turning turn a nut, turning gearsgears

TorqueTorque

How is torque measured?How is torque measured?

- lb- lb·ft (English) ·ft (English)

- N·m (SI)- N·m (SI)

Rearranging the Torque Rearranging the Torque EquationEquation

TT

F LF L

T= F (L) F = T / L L = T / FT= F (L) F = T / L L = T / F

TorqueTorque

How is torque calculated?How is torque calculated?

- T = (F)(L)- T = (F)(L)

- torque = applied force x lever - torque = applied force x lever armarm

- applied force - applied force lbs. or N lbs. or N

- lever arm - lever arm ft or m ft or m

Rotational MathlabRotational Mathlab

You use a force of 20 lbs on a car lug nut. The You use a force of 20 lbs on a car lug nut. The wrench (lever arm) is 24 inches long. What wrench (lever arm) is 24 inches long. What is the torque of the lug nut?is the torque of the lug nut?

24 inches X 24 inches X 1ft 1ft = 2 ft = 2 ft 12 inches12 inches

T = (F)(L) T = (F)(L) T = 20 lbs ( 2 ft) = 40 ft lbs T = 20 lbs ( 2 ft) = 40 ft lbs

Linear Math LabLinear Math Lab

You will be practicing mathematical You will be practicing mathematical concepts pertaining to:concepts pertaining to:

Vector and scalar quantitiesVector and scalar quantities

1M1 lab1M1 lab

Pre labPre lab- read the lab in the lab - read the lab in the lab notebooknotebook

-Fill in the blanks-Fill in the blanks

Lab quizLab quiz

Special SkillsSpecial Skills – reading a ruler and – reading a ruler and graphinggraphing

1M2 Lab1M2 Lab

PrelabPrelab- Use the lab notebook and read - Use the lab notebook and read the labthe lab

Fill in the blanksFill in the blanks

Lab QuizLab Quiz

Special skillSpecial skill: reading a protractor: reading a protractor

Work Cited Work Cited

Thanks to My Most beautiful fantastic daughter Thanks to My Most beautiful fantastic daughter who is just the most wondrous young lady ever who is just the most wondrous young lady ever (that I shall buy (hopefully) a present for (that I shall buy (hopefully) a present for Halloween because everyone knows that’s like Halloween because everyone knows that’s like the best holiday ever besides Christmas. And take the best holiday ever besides Christmas. And take out to dinner every night because she’s just out to dinner every night because she’s just smexy like that) for designing the WHOLE smexy like that) for designing the WHOLE powerpoint and making it very beautiful.powerpoint and making it very beautiful.

And also thanks to the unknown person whose And also thanks to the unknown person whose original powerpoint is the basis of this one.original powerpoint is the basis of this one.

And thanks to the colleague who gave it to me. And thanks to the colleague who gave it to me.