Force in Mechanical Systems

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 measuretape measure  Play the ruler gameruler 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) System

Force in Mechanical System How do we measure forces? How do we measure forces?  The English unit for force is the pound (lb.)  The metric unit for force is the Newton (N)

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

King Henry Doesn’t Mind Discussing Church Matters

International System (SI)  root units : meter liter gram  Base Units Base units are meter, kilogram, second,… Base Units Base Units  (see table 2 on page 6)  Kilo hecto Deka (root) deci centi milli  K H Da d c m  

Metric Activity You will need a meter stick Remember: -a millimeter is slightly less than a dime -a centimeter is width of a pinky finger -a decimeter is about a hand width -a meter is slightly longer than the distance from your nose to your finger tips

Changing Prefixes- 1  Make a chart K / H / Da / meter, liter, gram / d / c / m 378 cm to m The decimal moves 2 places to the left 3.78 m

Changing Prefixes - 2 Property of One  378 cm to m  100 cm = 1 m  378 cm X 1 m = 3.78 m cm cm

Force in Mechanical System What are other common units? SIEnglish Length meter (m) foot (ft) Time second (s) second (s) Mass kilogram Pound mass Weight Newton (N) Pound (lb) Mass & weight conversions - 1 pound = 4.45 Newtons - 1 kilogram weighs 9.8 Newtons

Assignments Measuring Activities Measuring Activities Linear Math 1 Linear Math 1

Mass vs Weight What is the difference between weight and mass? -Mass – the amount of matter in a -Mass – the amount of matter in a object object - measured in pound mass (lbm), grams or kg grams or kg -Weight – mass and the measure of the Earth’s gravitational pull Earth’s gravitational pull - measured in pounds (lb) or newtons

Force in Mechanical System Can mass change? - no, mass does not change Can weight change? -yes, weight can change as gravity changes Gravity is 1/6 less on the moon.

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

Gravity Varies with elevation Varies with elevation Mt Everest Mt Everest – weigh less Death Valley Death Valley – weigh more Would you weigh more or less in New Orleans? Would you weigh more or less in New Orleans? More you are below sea level More you are below sea level

Force in Mechanical System Are mass and weight the same thing? - no, mass and weight are very different

You weigh 120 lbs on Earth. What do you weigh on the moon? 20 lbs 20 lbs

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

Weight = mass X Gravity Variable English SI Weight W lbN Mass mlb-masskg Gravity g32 ft/s m/s 2

To convert mass to weight In our labs we convert mass/weight in SI EX: Use the Property of One 500 g X N = N 1 g 1 g 100 Kg X 9.81 N = 981 N 1 Kg 1 Kg

Convert Weight to mass EX: Use the Property of One EX: Use the Property of One 25 N X 1 kg = 2.55 Kg 9.81 N 9.81 N 4 N X 1 g = g 4 N X 1 g = g N N

Weight and mass math ws Weight and mass math ws

Vectors and Systems What two factors determine the effect of a force? - the strength of the force - direction of the force What is the strength of the force called? What is the strength of the force called? - Magnitude

Force in Mechanical System What is the difference between vectors and scalars? What is the difference between vectors and scalars? - a vector is a physical quantity that has both a magnitude and direction - forces, velocity, acceleration - a scalar quantity only has a magnitude - temperature, pressure, mass

Force in Mechanical System What is the difference between vectors and scalars? What is the difference between vectors and scalars? - a vector is a physical quantity that has both a magnitude and direction - forces, velocity, acceleration - a scalar quantity only has a magnitude - temperature, pressure, mass

Which are vectors???? 55 mph 55mph, E 55 mph 55mph, E 20 ft, left20 ft 20 ft, left20 ft 30 N at 20 degrees 30 N 30 N at 20 degrees 30 N 5 mm5 mm, down 5 mm5 mm, down

Answers to Vectors Any number with a direction Any number with a direction 55 mph 55mph, E 55 mph 55mph, E 20 ft, left20 ft 20 ft, left20 ft 30 N at 20 degrees 30 N* 30 N at 20 degrees 30 N* 5 mm5 mm, down 5 mm5 mm, down *Sometimes the unit indicates direction *Sometimes the unit indicates direction

How can we represent forces? - all vectors can be represented by arrows - the arrow length represents the magnitude of the force - the arrow heading represents the direction of the force Tail Head Tail Head

Force in Mechanical System Consider the example – A worker pulls a heavy cart with a force of 30 pounds at an angle of 30 o above the floor. Draw out this vector. 30 lbs 30 o

What is a balanced force? - forces that are equal in size and opposite in direction - THERE IS NO MOVEMENT example: two men pushing on a fence

What is an unbalanced force? - force that unequal in either size or direction - causes movement example – man pushing lawn mower, the mower moves

What is a net force? - the force that is leftover when all forces are taken into consideration A man pulls a rope with 5 N of force to the right. A second man pulls with 15 N of force to the left. What is the net force on the rope? - 10 N to the left

Are the forces on the rope balanced or unbalanced? - unbalanced Will the rope move? Will the rope move? - Yes, because an unbalanced force causes motion

Example – Four people are playing tug of war. Two people on one side pull against two people on the other side. The two on the right each pull with 50 pounds of force. The two on the left pull with 70 pounds of force. What is the net force? (magnitude and direction) 40 pounds of force to the right (net force)

Newton’s Laws

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

Newton’s 1 st Law of Motion (also Law of Inertia) An object at rest will remain at rest An object in motion will remain in motion Unless acted upon by an unbalanced force.

If a body is at rest and unbalanced forces (net force) act on it, what will happen? - the body will be accelerated in the direction of the force (Newton’s Second Law of Motion)

Newton’s 2 nd Law F = m a

If you push down a trampoline with 10 N of force, what how much force will push back on you? If you push down a trampoline with 10 N of force, what how much force will push back on you? - 10 N of force will push you up - Newton’s Third Law of Motion – for every action, there is an equal and opposite reaction

Newton’s 3 rd Law of Motion For every action there is an equal and opposite reaction

Adding Vectors

How do we add forces that act along the same line? - if the forces act in the same direction, we add magnitude of the forces - if the forces act in opposite directions, we subtract the magnitude of the forces

Vector Addition Joe’s car runs out of gas. Joe’s friend Anne helps Joe push the car into the gas station. Joe pushes with 200 lb and Anne pushes with 180 lb. What is the net force? 380 lb forward

What would happen if the two teams below both pulled with a force of 750 lb? - the rope would not move because the forces are balanced or in equilibrium

Force in Mechanical System How do we add forces that act at an angle? - you cannot add forces when they act at angles - you can solve them graphically What is the overall force when multiple forces are acting on an object? - a resultant force - the resultant always acts in a direction between the directions of the two forces

Graphical Analysis Vectors are drawn as accurate as possible. Vectors are drawn as accurate as possible. Rulers and protractors are used Rulers and protractors are used Used when you don’t use trigonometry Used when you don’t use trigonometry

Forces at Angles - Step One – Look at the force vectors - Choose scale for the line -for ex: 1 cm = 10 lb - use a ruler -Step Two- Place a dot on the paper - Step Three –Draw the two force vectors coming out of the dot while using the scale, ruler and protractor (Be sure you are drawing the vectors in the correct direction)

Force in Mechanical System -Step Four – Draw a parallelogram ALWAYS add the tail of the second vector to the head of the first vector -Step Five – Draw the resultant force- (the diagonal line from the dot to the end corner) -Step Six – Measure the length of the resultant (magnitude) and measure the angle on either side (direction) - use the ruler and protractor

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

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

Measure the Net Force Make a parallelogram and measure the net force (resultant) which is the diagonal line. Make a parallelogram and measure the net force (resultant) which is the diagonal line. measure the angles on either side of the dot measure the angles on either side of the dot 30 lbs 30 lbs 40 lbs 40 lbs

Answer The resultant or net force is the path that the boat will take The resultant or net force is the path that the boat will take Net force = 50 lbs ( the line was 5 inches) Net force = 50 lbs ( the line was 5 inches) Angles 53 o, 37 o Angles 53 o, 37 o

Torque What is torque? - the effect of a force applied on a body at some distance from the axis of rotation of that body - torque causes rotation What are two ways an object can rotate? - clockwise and counterclockwise

Torque When is torque used? - opening a paint can, opening a door, using a wrench to turn a nut, turning gears

Torque How is torque measured? - lb·ft (English) - N·m (SI)

Rearranging the Torque Equation T F L F L T= F (L) F = T / L L = T / F

Torque How is torque calculated? - T = (F)(L) - torque = applied force x lever arm - applied force  lbs. or N - lever arm  ft or m

Rotational Mathlab You use a force of 20 lbs on a car lug nut. The wrench (lever arm) is 24 inches long. What is the torque of the lug nut? 24 inches X 1ft = 2 ft 12 inches T = (F)(L) T = 20 lbs ( 2 ft) = 40 ft lbs

Linear Math Lab You will be practicing mathematical concepts pertaining to: You will be practicing mathematical concepts pertaining to: Vector and scalar quantities Vector and scalar quantities

1M1 lab Pre lab- read the lab in the lab notebook Pre lab- read the lab in the lab notebook -Fill in the blanks Lab quiz Lab quiz Special Skills – reading a ruler and Special Skills – reading a ruler and graphing graphing

1M2 Lab  Prelab- Use the lab notebook and read the lab  Fill in the blanks  Lab Quiz  Special skill: reading a protractor

Work Cited Thanks to My Most beautiful fantastic daughter who is just the most wondrous young lady ever (that I shall buy (hopefully) a present for Halloween because everyone knows that’s like the best holiday ever besides Christmas. And take out to dinner every night because she’s just smexy like that) for designing the WHOLE powerpoint and making it very beautiful. Thanks to My Most beautiful fantastic daughter who is just the most wondrous young lady ever (that I shall buy (hopefully) a present for Halloween because everyone knows that’s like the best holiday ever besides Christmas. And take out to dinner every night because she’s just smexy like that) for designing the WHOLE powerpoint and making it very beautiful. And also thanks to the unknown person whose original powerpoint is the basis of this one. And thanks to the colleague who gave it to me.