Today A pictorial way to calculate rates of changebogner/isp209s2010/lectures/l3p.pdf · ... (Newton’s 1st Law) •What is Force? ... object will keep moving with a constant velocity

ISP209s10 Lecture 3 -1-

Today

• Announcements:

– HW#2 and extra credit #1 is due Wednesday1/27 by 8:00 am

– Pls. register your clickers on LONCAPA

• Loose ends from last class

• Law of Inertia (Newton’s 1st Law)

• What is Force? Introduction


A pictorial way to calculate rates of change

• Draw a line tangent

to the curve at the time

you want. The line can

be any length.

• Mark two points on

the line and record the

values.

• Calculate the slope of

the tangent line

sm

tt

ddspeedm 59.0

5.23.9

26

12

12 =!

!=

!

!==


Speed versus distance plot

Example: Motion of a car as a function of time.

We can get this graph from this one by repeating the previous

calculation for several different times and plotting the points


Homework Problem Traveling Car

1st sketch the

speed vs. time

graph

Next, use the

speed graph to

sketch the

acceleration vs.

time graph


Adding and Subtracting 2 Vectors

• Imagine two vectors (A and B)represent two walks, one in one

direction and the other in another direction.

• A negative sign means "go the opposite direction the arrow

shows".

• The resultant vector (C) points from your original starting point

to where you ended up at the end of the second walk.



Example 1:



Example 2:


History of our effort to understand motion

• Aristotle(384 BC – 322 BC)– Natural motions: items seek their natural locations

– Violent motions like moving across the room require an agent

• Galileo (1564-1642)– Tried to deduce the laws of motion from experiments

– Introduced the concept of inertia. (Inertia is not a well definedconcept.)

• Isaac Newton (1643-1727)– Formulated laws that govern planetary motion and most** motion

we see in our daily lives

– Invented Calculus along the way

– Many view Newton (along w/Einstein) as the “greatest” ever

** Except for the very small (Quantum Mechanics) and fast (Special Relativity)


• Aristotle distinguished three kinds of motion

• Natural motion: falling objects and liquids, rising

air and flames

• Violent motion: needing a constant push or pull to

continue

• Celestial motion: motion of the moon, planets, sun,

and stars

Aristotle’s “Common Sense” Theory of Motion


Now, throw a ball across the room. Once it leaves your

hand, what keeps it moving? Aristotle says there must

be a constant force to keep it in motion.

Sounds like common sense, no?

Problems with Aristotle’s Theory

We saw last lecture that our “common sense” or

intuition can be totally wrong…


Galileo’s thought experiment: Let a ball roll down an incline; it

will speed up. Let it roll up the incline; it will slow down. In

between, on a perfectly flat surface with no friction, the ball will

keep rolling at a constant speed forever.

Galileo’s Thought Experiment


Galileo’s method:

• Experimentation, to test a specific hypothesis

-E.g., Aristotle’s theory of falling objects

• Idealization, to eliminate side effects that may mislead

-E.g., air resistance and friction

• Consider only one question at a time

- E.g. speed of falling objects of different masses

• Quantitative methods: precise measurement

- E.g., timing the fall of different objects from a tower

Galileo and the Scientific Method


• Imagine we could turn off air resistance, friction, and

gravity. How would things move?

• Descartes had the answer (which Newton took as his first

principle of motion):

The Law of Inertia: A body that is subject to no external

influences (also called external forces) will stay at rest if

it was at rest to begin with and will keep moving if it was

moving to begin with; in the latter case, its motion will be

in a straight line at an unchanging speed.

The Law of Inertia


• For example, if you are driving a car on an icy

road – a VERY icy road – and try to stop or turn,

you will find that your car continues to go in a

straight line, as there is little friction.

• You can also watch videos of astronauts – they

will float in a straight line with constant speed

(unless something pushes/pulls them)

The Law of Inertia


• The law of inertia tells us that an undisturbed

object will keep moving with a constant velocity.

• If an object’s velocity is changing, it is

accelerating. Acceleration is the rate of change of

velocity:

acceleration = (change in velocity)/time

Acceleration and the Law of Inertia


• Falling objects accelerate as they fall.

• How do we know this? Hold your book above

the floor and let it drop.

• What is its speed right when you let it go?

(Don’t throw it!) What is its speed when it hits

the floor?

Falling


• This diagram shows an object

falling.

•Note that both its distance and its

velocity are increasing.

•From one second to the next, the

distance traveled increases, but the

change in velocity is the same.

Falling


• We see that the speed is proportional to the time –

10 m/s at 1 s, 20 m/s at 2 s, and so forth.

• What about the distance? Clearly it is not

proportional to the time.

• However, if we look at the pattern of how the

distance changes from second to second, we can see

that the distance is proportional to the square of the

time.

Falling


• The object in the diagram is changing its speed

at a rate of 10 m/s per second. Therefore, its

acceleration is 10 m/s2.

• This is (approximately) the acceleration due to

gravity anywhere on the Earth.

• It does NOT depend on the mass, size, or shape

of the object. Aristotle was wrong.

Falling

Click HERE for a demonstration using a coin and featherISP209s10 Lecture 3 -20-

What is a Force?

• A force is a push or pull.

• Force is a vector, it has a magnitude and a direction.

• A better definition is given by Newton’s Three Laws ofForce (my versions)

– If the net force on an object is zero the object will notaccelerate.

– The amount of acceleration depends on the mass of the object

and the amount of the applied force: F = ma .

– For every force, there is an equal and opposite force.

• Improved definition: Force is the rate of change ofmomentum.


How much force?

Neglecting friction from the air, a 80.0 kg professor

falls off a bench and accelerates toward the ground at

9.81 m/s2.

What is the magnitude of the force of gravity on the

professor?

F = mass x acceleration = 80.0 kg x 9.81 m/s2 = 785.

N


• Undisturbed objects will continue moving in a straight

line with constant speed (Law of Inertia, aka Newton’s

1st Law )

• any change in speed or direction (I.e., acceleration)

must require a force.

• Force is an action, such as a push or pull, rather than

a thing. A force is exerted on one object by another.

Force: Why Things Accelerate


Is it possible to have a force without acceleration?

Only if there are two forces that cancel each other out.



• If you kick a football, when does it accelerate? If

you watch carefully, you will see that the ball only

accelerates while your foot is in contact with it.

• Other forces: friction, air resistance – these both

act to slow moving objects

• Gravity: force exerted by the Earth (due to its very

large mass)


A bit different then the previous examples.

Nothing is “touching” an apple to make it

fall. Gravity acts at a distance across space.


Through experimentation, we see that the acceleration is

proportional to the force:

a ! F

Connecting Force and Acceleration


• Inertia is not the same as weight

• Imagine being in outer space. Nothing has

weight, but objects still have inertia – they will

resist a pull or push.

• Mass is the quantitative measure of inertia. In

the metric system, mass is measured in kilograms.



Through experimentation, we see that the same force

produces a smaller acceleration of a greater mass.

Acceleration is inversely proportional to mass:

a ! 1/m.



So, we have found that acceleration is proportional

to force and inversely proportional to mass:

a ! F/m

One newton (N) is defined as the force it takes to

accelerate 1 kg at 1 m/s2; using these units, we can

write:

a = F/m



What is a force on a deeper level?

• These laws let us recognize a force, but whatcauses a force?

– Modern view is related to Quantum Field Theory.

– Forces are the result of an exchange of “virtual”particles that pop in and out of existence from“thin air”.

• To understand field theory, we have to talkabout energy and quantum mechanics (later inthe term).

Documents

Today A pictorial way to calculate rates of changebogner/isp209s2010/lectures/l3p.pdf · ... (Newton’s 1st Law) •What is Force? ... object will keep moving with a constant velocity