Physics 151: Lecture 7, Pg 1 Physics 151: Lecture 7 Today’s Agenda l Announcements: çHomework #2...

Physics 151: Lecture 7, Pg 1

Physics 151: Lecture 7Physics 151: Lecture 7Today’s AgendaToday’s Agenda

Announcements:Homework #2 : due Fri. (Sept. 15) by 5.00 PM

Homework #3 : due Fri. (Sept. 22) by 5.00 PM

Physics learning Center (P207-C) Mon.-Fri 9 am - 5pm

Review sessions:

Today’s topicsNewton’s Laws 1 and 2 (Chapter 5.1-4)


KYNEMATICS (previous chapters):

description of motion: r(t), v(t), a(t)

DYNAMICS (next chapter):

what makes the objects move the way they do, learn about forces and how to calculate just what acceleration is.


EXAMPLE from EVERYDAY LIFE : A passenger sitting in the rear of a bus claims that he was

injured when the driver slammed on the brakes, causing a suitcase to come flying toward the passenger from the front of the bus.

• Do you agree with this statement ?


Isaac Newton (1643 - 1727)published Principia Mathematica in 1687.


DynamicsDynamics

Isaac Newton (1643 - 1727) published Principia Mathematica in 1687. In this work, he proposed three “laws” of motion:

Law 1: An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame.

Law 2: For any object, FFNET = FF = maa

Law 3: Forces occur in pairs: FFA ,B = - FFB ,A

(For every action there is an equal and opposite reaction.)

See text: Chapter 5


ForceForce

We have an idea of what a force is from everyday life.

Physicist must be precise. A force is that which causes a body to accelerate.

(See Newton’s Second Law)

Examples

Contact Non-Contact

On a microscopic level, all forces are non-contact

See text: 5-1

Question: What force causes an automobile to move ?


MassMass We have an idea of what mass is from everyday life.

Physicist must be precise. mass (for this class) is a quantity that specifies how much

inertia an object has.

(See Newton’s First Law)

Mass is an inherent property of an object.

Mass and weight are different quantities.

weight is a force.

See text: 5-3

Animation


Newton’s First LawNewton’s First LawAn object subject to no external forces moves with a constant velocity if viewed from an inertial reference frameinertial reference frame.

If no forces act, there is no acceleration.

The above statement can be thought of as the definition of inertial reference frames.An IRF is a reference frame that is not accelerating (or rotating) with respect to the “fixed stars”.If one IRF exists, infinitely many exist since they are related by any arbitrary constant velocity vector!

See text: 5-2


Is Storrs a good IRF?Is Storrs a good IRF?

T = 1 day = 8.64 x 104 sec, R ~ RE = 6.4 x 106 meters .

Plug this in: aS = .034 m/s2 ( ~ 1/300 g) Close enough to 0 that we will ignore it. Storrs is a pretty good IRF.

RT2

RRv

a22

S

2

Is Storrs accelerating? YES!

Storrs is on the Earth.The Earth is rotating.

What is the centripetal acceleration of Storrs?


Question / Newton’s First Law Question / Newton’s First Law

See text: 5-2

What is wrong with this statement, "Because the car is at rest, there are no forces acting on it” ?

Mistake one: The car might be momentarily at rest, in the process of (suddenly) reversing forward into the backward motion. In this case, the forces on it add to a (large) backward resultant.

Mistake two: There are no cars in interstellar space. If the car is remaining at rest, there are some large forces on it, including its weight and some force or forces of support.

Mistake three: The statement reverses cause and effect.


Newton’s Second LawNewton’s Second Law

The acceleration of an object is directly proportional to the net force acting upon it. The constant of proportionality is the mass.

See text: 5-4

amFFNET

UnitsThe units of force are kg m/s2 = Newtons (N)The English unit of force is Pounds (lbs)


Lecture 7,Lecture 7, ACT 1ACT 1Newton’s Second LawNewton’s Second Law

I push with a force of 2 Newtons on a cart that is initially at rest on an air table with no air. I push for a second. Because there is no air, the cart stops after I finish pushing. It has traveled a certain distance (before removing the force).

For a second shot, I push just as hard but keep pushing for 2 seconds. The distance the cart moves the second time versus the first is (before removing the force) :

A) 8 x as long B) 4 x as long C) Same

D) 2 as long E) can’t determine

Air Track

CartF= 2N


Lecture 7Lecture 7, , ACT 1ACT 1

B) 4 x as long

Air Track

CartF= 2N

t1 =1s, v1 t2 =2s, v2to , vo = 0

Cart Cart

x1 x2




Lecture 7Lecture 7, , ACT 1aACT 1a

Air Track

Cart CartCartFapp

at rest

What is the distances traveled What is the distances traveled afterafter F Fappapp removed in the two cases: removed in the two cases:

(i) after applying F(i) after applying Fappapp for 1 s for 1 s vs. vs.

(ii) after aplying F(ii) after aplying Fappapp for 2 s ? for 2 s ?




Lecture 7Lecture 7, , ACT 1aACT 1aWhat is the distances traveled after FWhat is the distances traveled after Fappapp removed ? removed ?

Air Track

Cart

to , vo1

to , vo2

Cart

Air Track

Cart Cart

t1 , v1 = 0

t2 , v2 = 0

Cart

Cart

Fapp= 2N

x1

x2

Fapp = 0

Fapp= 2NFapp = 0

Ftot = 0 ?

Ftot = 0 ?

at rest

at rest

otherwise v1=v01, cart keeps moving !

B) 4 x as long


Lecture 7Lecture 7, , ACT 2ACT 2Newton’s Second LawNewton’s Second Law

A) the body will stop moving.B) the body will move in the direction of the force.C) the body’s velocity will increase in magnitude but not change direction.D) the body will gradually change direction more and more toward that of the force while speeding up.E) the body will first stop moving and then move in the direction of the force.

F A constant force is applied to a body that is

already moving. The force is directed at an angle of 60 degrees to the direction of the body’s velocity. What is most likely to happen is that:

vo

60o


Newton’s Third Law:Newton’s Third Law:

If object 1 exerts a force on object 2 (F1,2 ) then object 2 exerts an

equal and opposite force on object 1 (F2,1)

F1,2 = -F2,1

See text: 5-6

This is among the most abused and misunderstood concepts in physics, along with Einstein’s ideas of relative motion (inertial reference frames) and Heisenberg’s uncertainty principle.

For every “action” there is an equal and opposite “reaction”


Newton's Third Law...Newton's Third Law...

"When the locomotive in Figure on the right broke through the wall of the train station, the force exerted by the locomotive on the wall was greater than the force the wall could exert on the locomotive.”

Is this statement true or in

need of correction?

See text: 5-6

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.


An ExampleAn Example

FB,E = - mB g

FE,B = mB g

Consider the forces on an object undergoing projectile motion


Lecture 7, Lecture 7, ACT 3aACT 3aNewton’s Third LawNewton’s Third Law

A fly gets smushed onto the windshield of a speeding bus.

The force exerted by the bus on the fly is,A) greater thanB) the same asC) less than

that exerted by the fly on the bus.


Lecture 7, Lecture 7, ACT 3bACT 3bNewton’s Third LawNewton’s Third Law

A fly gets smushed onto the windshield of a speeding bus.

The acceleration due to this collision of the bus is,A) greater thanB) the same asC) less than

that of the fly.


Newton's Third Law...Newton's Third Law...

FFA ,B = - FFB ,A an example,

FFm,w FFw,m

FFm,f

FFf,m

See text: 5-6


Example of Bad ThinkingExample of Bad Thinking

Since FFm,b = -FFb,m why isn’t FFnet = 0, and aa = 0 ?

a ??a ??FFm,b FFb,m

ice


Example of Good ThinkingExample of Good Thinking

Consider only the box only the box as the system!Free Body Diagram

FFm,b FFb,m

ice


Example of Good ThinkingExample of Good Thinking

Consider only the box only the box as the system!Free Body Diagram

aaboxbox

FFb,m

FgFN

abox = Fb,m/mbox


Normal ForcesNormal Forces

Certain forces act to keep an object in place. These have what ever force needed to balance all others

(until a breaking point).

FT,B

FB,T


Force PairsForce Pairs

Newton’s 3rd law concerns force pairs. Two members of a force pair cannot act on the same object.

Don’t confuse gravity (the force of the earth on an object) and normal forces. It’s an extra part of the problem.

FT,B

FB,T

FB,E = -mg

FE,B = mg



Consider the following two cases



The Free Body Diagrams

mg

mg

FB,T= N

Ball FallsFor Static Situation

N = mg



The action/reaction pair forces

FB,E = -mg FB,T= N

FE,B = mg

FB,E = -mg

FE,B = mg

FT,B= -N


Recap for today:Recap for today:

Definition of force and mass (Ch. 5.1 and 5.3)

Newton’s Laws

Reading assignment for MondayNewton’s Laws 2 and 3



Physics 151: Lecture 7, Pg 1 Physics 151: Lecture 7 Today’s Agenda l Announcements: çHomework #2...

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