Chapter 4

Dynamics: Newton’s Laws of Motion

Kinematics: measure how things moveDynamics: understand why things move

Quiz for Felix Buamgartner jump -- 14 Oct 2012

1. Started at 128,100 ft above earth = 39.0km

2. Reached ~729 mph after ~48 seconds = 326m/s

3. Calculate average a. 6.79m/s2

4. Would you expect a to be constant? Why?

5. Is it higher or lower than g? Why?6. How far does he fall in 48 s? Can’t know since a isn’t constant.

Units of Chapter 4

•Some history of physics

•Force

• Newton’s First Law of Motion

• Mass

• Newton’s Second Law of Motion

• Newton’s Third Law of Motion

• Weight – the Force of Gravity; and the Normal Force

• Solving Problems with Newton’s Laws: Free-Body Diagrams

• Applications Involving Friction, Inclines

• Problem Solving – A General Approach

Units of Chapter 4

Some forces and some accelerations

• Fan car

• Spring release

• Coil spring pulling lab cart

• Air pushing ping pong ball– Take data: ball mass = 2.55g– Tube length = 3.0 m– Room pressure = 101,000 N/m2

– Vacuum pressure = 5,000 N/m2

Physics before Newton• Aristotle: 4th century b.c.• A philosopher before science existed

– Valued reason over observation– Example -- Motion:– Student: why does the cloud fly up there?– Aristotle: it is in the clouds nature to go up.– Student: so the cart will be hard to push because that

is its nature? I don’t have to test it?– Aristotle: you are wise, grasshopper. And why would

you bother yourself with an experiment when you could sit here under the olive tree and eat grapes?.

• This thinking lasted 2000 years until Newton!

Galileo Galilei 1564-1642

• Studied and observed and experimented in physics

• Kinematics: proved that things accelerate when they fall, and measured g

• Proved that this g is independent of mass

• Got into big trouble for challenging The (Roman Catholic) Church in astronomy

• Wrote funny books to make his point

Isaac Newton, 1642-1728

– Born on English farm the year Galileo died

– Studied natural philosophy at Cambridge U.

– Invented calculus to solve problems in astronomy and other fields

– Did major work in optics

– Developed laws of motion

– All this before he was 25 years old!

– The Principia summarized all his major work

And he had a nice wig.

And he studied alchemy.

And he was cranky and unkind to almost everyone.

Genius isn’t easy.

4-1 Force

A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity.

The magnitude of a force can be measured using a spring scale.

4-2 Newton’s First Law of Motion

Newton’s first law is often called the law of inertia.

Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no

net force acts on it.

4-2 Newton’s First Law of Motion

Inertial reference frames:

An inertial reference frame is one in which Newton’s first law is valid.

This excludes rotating and accelerating frames.

Everything we do will be in an Inertial reference frame, so Newton’s laws will be valid.

4-3 Mass

Mass is the measure of inertia of an object. In the SI system, mass is measured in kilograms.

Mass is not weight:

Mass is a property of an object. Weight is the force exerted on that object by gravity.

If you go to the moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same.

Calculate your mass in kg.

4-4 Newton’s Second Law of Motion

Newton’s second law is the relation between acceleration and force. Acceleration is proportional to the net force and inversely proportional to mass.

(4-1)F = maF is a vector!a is a vector!m is not a vector!

F is a vector!a is a vector!m is not a vector!

Does the object accelerate in same direction as the force?

4-4 Newton’s Second Law of Motion

Force is a vector, so is true along each coordinate axis.

The unit of force in the SI system is the Newton (N).

Note that the pound is a unit of force, not of mass, and can therefore be equated to newtons but not to kilograms.

Fx = max

In class demo with force• Brass Weights, string, spring scale, board• Hook up and pull gently• Do the following

– Apply force but no motion– Accelerate on the table vs. constant speed– Constant speed on table vs. on flat board– Flat board vs. angled board

• In each case identify and quantify all the forces on the brass weight

• Record in your notebook.

4-5 Newton’s Third Law of Motion

Any time a force is exerted on an object, that force is caused by another object.

Newton’s third law:

Whenever one object exerts a force on a second object, the second exerts an equal force in the

opposite direction on the first.

4-5 Newton’s Third Law of Motion

A key to the correct application of the third law is that the forces are exerted on different objects.

Show the sled paradox: example 4-5

Newton’s Third Law – define reaction forceRocket propulsion can also be explained using Newton’s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket.

Note that the rocket does not need anything to “push” against.

20 oct: 4-5 Newton’s Third Law of MotionHelpful notation: the first subscript is the object that the force is being exerted on; the second is the source.

(4-2)

Always always identify the object you are analyzing!

The simple fan car demo

• Neglect friction

• Measure F

• Measure m

• Measure a with gomotion

• Do they agree?

27 oct: 4-6 Weight – the Force of Gravity; and the Normal Force

Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight is:

What is your mass?What is your weight?

4-6 Weight – the Force of Gravity; and the Normal Force

An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there?

The force exerted perpendicular to a surface iscalled the normal force. It is exactly as large as needed to balance the force from the object (if the required force gets too big, something breaks!)

Another demo with a force

• Hold ball, measure F with “force sensor”– What is another name for this force we

measured?

• Drop ball

• Measure y, v, a with go motion

• Does a = F/m?

• What is normal force in this case?

In class check: forces

• Fan car accelerates on table top

• What are all the forces on the car?

• What are all the forces on the air?

• What are all the forces on the table?

• F of fan = 1.5N

• M of cart = 250g

• F of friction = 0.3N

• What is a?

4-7 Solving Problems with Newton’s Laws – Free-Body Diagrams

1. Draw a sketch.

2. choose one object, draw a free-body diagram, showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each one.

3. Identify which way is positive in each dimension

4. Resolve vectors into components.

5. Apply Newton’s second law to each dimension.

6. Use Ff = FN if necessary

7. Solve for unknown

4-7 Solving Problems with Newton’s Laws – Free-Body Diagrams

When a cord or rope pulls on an object, it is said to be under tension, and the force it exerts is called a tension force.

Practice FBD problems

• Push Box on Frictionless table

• Pull box with rope at angle

• Piano sliding down ramp

• Weight hanging in middle of rope

After reading your notes• Many are impressive, some poor• Suggestions:

a. Use headings: what’s the topic, the goal

b. Use boxes, bubbles, color to capture side notes

c. Use more paper, spread it out

d. If I say something twice, underline it. If thrice, twice.

e. If my point isn’t clear, mark with big ???, or ask me!

f. Use symbols: !, ?, o, !%#*!?!*

g. Write the checklist and the classics list

h. Tab important pages with tape

i. Save a page for tips/advice/comments each chapter

j. Use more color, esp for vectors

k. Do algebra after class, don’t rush it in class

l. Star or highlight the classics that we do in class

Frictionless box on the floor• Box mass m, with HORIZONTAL force FA. What is a?

F=ma

– FA/m = a

• Version B: same box, with F at an ANGLE . What is a?

– Just need to resolve the force.

Piano on ramp, no friction• Piano mass m on ramp of angle . • What is acceleration down the ramp?• Draw FBD, resolve forces

• Find Fx, and set Fx = max

Now consider Friction

• examples to consider– Air puck– Bike wheel– Block on tabletop– Interlaced book pages

• Measure with force meter– Lead masses on table top

4-8 Friction between surfacesOn a microscopic scale, most surfaces are rough. The exact details are not yet known, but involve molecular bonding: The force can be modeled in a simple way.

For kinetic – sliding – friction:

is the coefficient of kinetic friction, and is different for every pair of surfaces.

4-8 Applications Involving Friction

4-8 Applications Involving Friction

Static friction is the frictional force between two surfaces that are not moving along each other. Static friction keeps objects on inclines from sliding, and keeps objects from moving when a force is first applied.

When could the force of friction be less than sFN?

The static frictional force increases as the applied force increases, until it reaches its maximum.

Then the object starts to move, and the kinetic frictional force takes over.

4-8 Applications Involving Friction

31 oct: 4-8 Applications with Inclines

An object sliding down an incline has three forces acting on it: the normal force, gravity, and the frictional force.

• The normal force is always perpendicular to the surface.

• The friction force is parallel to it.

• The gravitational force points down.

If the object is at rest, the forces are the same except that we use the static frictional force, and the sum of the forces is zero.

Demo force plate

• Push table from stop to go– Plot F vs. t

• Push table with more mass on it

A range of forces

• Weight mg

• Normal FN always perp to surface

• Applied FA

• Tension T

• Friction FFr or FS or FKAre they all vectors?

FORCES THAT MATTER FA applied (can push or pull)T tension (can only pull, not push)FN normal (perpendicular to surface)mg weight (always points down)Fs static friction (parallel to surface)Fk kinetic friction (parallel to surface)

Accelerations that matterac centripetalax translational xay translational y

Equations that helpFx = max for each dimensionFfr = FN for static or kinetic

Quiz 29 Oct.

• A fan car, mass M = 13.4kg, gets pushed by the fan with force of F = 1.90N on a flat table. The force of friction Ff is 0.22N.

1.Draw FBD

2.Write a symbolic formula for acceleration in terms of given quantities

3.Calculate acceleration with sig figs

4.Calculate the coefficient of friction

More problems to know

• Box sliding with friction on flat floor

• Skier with friction, what is • Parachutist at terminal velocity

Box with friction on ramp, find a• Same setup as skiier finding k

• Angle , mass m

• Resolve vectors, use FF = FN

Parachute guy• Man mass m with parachute falling at terminal velocity. F = ma leads to mg – FF = ma, and at terminal velocity

a=0.

Weigh yourself on an elevator• You mass m, elevator going up at a, what is FN

Fy = may

4-9 Problem Solving – A General Approach

1. Read the problem carefully; then read it again.

2. Draw a sketch, and then a free-body diagram.

3. Choose a convenient coordinate system.

4. List the known and unknown quantities; find relationships between the knowns and the unknowns.

5. Estimate the answer.

6. Solve the problem without putting in any numbers (algebraically); once you are satisfied, put the numbers in.

7. Keep track of dimensions.

8. Make sure your answer is reasonable.

The classic problems

1. Frictionless box on the floor, pull with rope

2. Frictionless Piano sliding down the ramp

3. Box with friction s on ramp, find 1. Also like Ski with friction, find terminal speed

4. Weigh yourself on the elevator

5. Parachute guy

6. Hang a weight on a rope

Not classic, but fun: box on table and box over edge with pulley

Hang a weight on a rope• Mass of m on the middle of a rope• Pulls down at angle from the horizontal• What is tension T of the rope?• Do FBD and F = ma in each direction x and y• Resolve forces, not that 2Tsin is pulling up

Lab: F=ma on a cart

• This lab includes practice and grading of your ability to collect contemporaneous notes.

• Part 1: you observe lab, and take notes of all parts (see handout)

• Part 2: you observe analysis, and take notes that explain each part.

• Part 3: you finish analysis in class, on your notes

• Turn in notes at end of class for grading.

Box on table pulled by box hanging down

• Both have mass m, find a of each

• Do FBD of each body, and recognize that ax for one is ay for the other and T is same for each box

• T = ma for the horizontal box• -T + mg = ma for the vertical box• So, a = ½ g

F = ma on the body

• Strong forces put the human body into high accelerations.

• We’ll study collisions later (momentum)

• Rockets and Jets are limited by how many g’s the pilots and passengers can survive.

• Let’s look at this powerpoint to see more….NASA report on effects of g forces.pptx

Summary of Chapter 4

• Newton’s first law: If the net force on an object is zero, it will remain either at rest or moving in a straight line at constant speed.

• Newton’s second law:

• Newton’s third law:

• Weight is the gravitational force on an object.

• The frictional force can be written:

(kinetic friction) or (static friction)

• Free-body diagrams are essential for problem-solving

Mid-term checkup with Dr. F

• Find 3 min to individually meet with me.

• It helps me adjust my teaching

• And I like to hear how you’re doing in the first term of a totally new class

• Do your parents share the comments of conferences?