Physics 218, Lecture VII 1

Physics 218Lecture 7

Dr. David Toback

Physics 218, Lecture VII 2

Physics 218, Lecture VII 3

Before we begin

• Exam Next Tuesday– Only on topics through Chapter 3 on

Syllabus• Not circular motion!

• Today’s lecture not on the exam• However, I’ll try to make it a good

review

Physics 218, Lecture VII 4

Overview of Chapter 4

• Where we’re going and why–Dynamics vs. Kinematics

• Force• Newton’s Laws of Motion• Mass• Normal Force• Example problems

Physics 218, Lecture VII 5

Where we’re going and why

Moving from: “How things move” Kinematics To: “Why things move that way” Dynamics• Why do you care?

– You know how to calculate how fast you need to accelerate a car if you want it to go from 0 to 60mi/hr in 6 sec.

– What you need to know is how hard the engine needs to work to do it. What FORCE you need.

• This builds on all the kinematics, vectors and calculus we’ve done before.

• We’ll develop the concepts, then learn to solve the problems.

Physics 218, Lecture VII 6

Newton’s Laws

• Next we’ll do Newton’s laws• You shouldn’t memorize them, rather you

need to be able to understand and use them• Don’t write them down from the

transparencies, they’re in your book.• We’re going to translate them into English• Big picture:

Force

Physics 218, Lecture VII 7

Before we start

What is a Force?

• Examples:– Push

– Pull

– Slap

– Gravity

– Others?

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Newton’s First Law

“Every body continues in it’s state of rest or of uniform speed in a

straight line unless acted on by a non-zero net force”

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Translate that into Engligh:Force

To cause an acceleration requires a Force

or If there is an acceleration, there

must be a Force

Force is a VectorAdd up all the forces (vectors) to find the Net force

Physics 218, Lecture VII 10

Newton’s First Law

• Example of non-zero net forces? – Friction: Causing a rolling ball to stop

– Gravity making a ball fall• (Net force causes acceleration in the

negative direction)

• Example of zero net force– Car sitting on the pavement

• No acceleration, must be no net force

Physics 218, Lecture VII 11

Newton’s Second Law

“The acceleration of an object is directly proportional to the net

force acting on it and is inversely proportional to its mass. The

direction of the acceleration is in the direction of the net force

action on the object.”

Physics 218, Lecture VII 12

Newton’s Second Law

• Translate this into English:– Net forces cause

the velocity to change

If I have a force, what is my acceleration? Need the mass.

gmWWeight

ma F ,ma F

am F

:EquationVector

yyxx

Physics 218, Lecture VII 13

Force to stop a car

What constant net force is required to bring a car of mass m to rest from a speed of V within a distance of XF?

X = 0 X = XF

V0 = V V = 0

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Getting to Newton’s Third Law

• How does one apply a force?

• Applying a force requires another object!–A hammer exerts a force on a nail

Physics 218, Lecture VII 15

Newton’s Third Law

“Whenever one object exerts a force on a second object, the second

exerts an equal and opposite force”

OR

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

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Example

Skater pushes on the wall. The wall pushes back, that’s why she flies off with some non-zero speed.

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Examples

Force exerted by the person on the ground is equal and opposite to the force exerted by the ground on the person. She pushes on the ground and the ground PUSHES her forward

PGGP F- F

Physics 218, Lecture VII 18

Normal Force

Consider a pen on a table:– What about Gravity? Didn’t we just say that a

pen near the earth would be accelerating due to gravity?

– What is the acceleration?– What is the Force?– What keeps the pen from accelerating?

Clearly there is a force which keeps it from accelerating.

Call this the “normal” force!

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Moving towards Problems

We’re now done with the concepts for this chapter

• This is where the separation between the good students and bad students starts to get noticeable.

• “I understand the concepts, but I can’t do the problems”

• Just to be clear: The concepts were only the first half of the lecture. No points on the exams for knowing “concepts you can’t apply”

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Free Body Diagrams

This is the trick: 1. Draw all the forces on an object!2. Then do the summing!3. Sum all the forces in the X direction and the Y

direction separately!!!

• This is a GREAT way to pick up partial credit on an exam problem.

• If you don’t know how to draw a force diagram, you don’t know how to solve the problem.

Physics 218, Lecture VII 21

The weight of a boxA box with mass m is resting on a

smooth (frictionless) horizontal table.

a) Determine the weight of the box and the normal force

b) Push down on it with a force of FP. What is the normal force?

c) Pull up on it with a force of FP such that it is still sitting on the table. What is the normal force?

d) Pull up on it with a force such that it leaves the table and starts rising. What is the normal force?

Physics 218, Lecture VII 22

Pulling a box

FP

A box with mass m is pulled along a frictionless horizontal surface with a force FP at angle as given in the figure. Assume it does not leave the surface.

a)What is the acceleration of the box?

b)What is the normal force?

Physics 218, Lecture VII 23

Box on an inclined planeA box with mass m is placed on a frictionless incline

with angle and is allowed to slide down.

a) What is the normal force?

b) What is the acceleration of the box?

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2 boxes connected with a stringTwo boxes with masses m1 and m2 are placed on a

frictionless horizontal surface and pulled with a Force FP. Assume the string between doesn’t stretch.

a)What is the acceleration of the boxes?

b)What is the tension of the strings between the boxes?

Physics 218, Lecture VII 25

Atwood Machine

Two boxes with masses m1 and m2 are placed around a pulley with m2 >m1

a) What is the acceleration of the boxes?

b) What is the tension of the strings between the boxes?

Ignore the mass of the pulley, rope and any friction. Assume the rope doesn’t stretch.

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Next Time

• No Exam Thursday

• Thursday: Make sure you read

– Section 3-9: Uniform Circular motion

– Chapter 5: More force and friction

– There will be a quiz.

• Finish HW 3 to study for Exam

• Labs/Rec/Web quizzes as usual

Physics 218, Lecture VII 27

How to study for the exam

• Do all the HW problems

• 4 Problems. Dominated by Chapter 3, almost nothing from Chapter 1.

• Make sure you can do all the HW problems easily and by yourself with no numbers

• Concentrate on the “hardest” problems. Those will be the most like the ones on the exam.

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Example 1

Force to accelerate a fast car

Estimate the net force needed to accelerate a 1000kg car at ½g

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Hockey Puck

• Which of these three best represents a hockey puck in the real world?

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Example 4-16

Physics 218, Lecture VII 31

Before we begin

• Exam Thursday– Formula sheet to be passed out is already on

web– Here at 8:00AM– Only on topics through Chapter 3 on

Syllabus• Not circular motion!

• Today’s lecture not on the exam• However, I’ll try to make it a good

review

Physics 218, Lecture VII 32

Mass vs. Weight• Mass is a property of the body

– Aside: What is mass is a fundamental question at the forefront of physics today. Particle physics! String theory!

• Weight is a Force and depends on the mass

What is the difference between:– Your mass on the moon and the earth?– Your weight on the moon and the earth?– Your weight in a space ship and the earth?

j mg- mg F W Weight earth on the weight of Definition

G

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Next Time• Exam Thursday: Here during regular time

– Bring a calculator and ruler– Formula sheet will be provided (same as on the

web)– Will cover:

• Chapter 1 (1-6)• Calculus 1• Chapter 2 (1-7)• Chapter 3 (1-8, 10)

• Finish HW 3 to study for Exam• Labs/Rec/Web quizzes as usual