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31-Aug-10 Physics 101

Lecture 4Chapters 3-4

Free FallNewton’s Second Law

Weight & GravityFriction

Quiz Friday -- Chapters 2 & 3


Velocity in Free Fall (Up & Down)

Moving upward, with each second the speed decreases by 10 meters/second.

Going back down the motion exactly reverses itself.

See Fig. 3.8 (pg. 43)

Zero m/s10 m/s

20 m/s

30 m/s

40 m/s

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Position in Free Fall

How far do objects go when they fall?

More complicated because speed is increasing.

There’s a pattern & Galileo figured it out.

But it wasn’t easy.

5 m

20 m

45 m

Release1 s

2 s

3 s

4 s 80 m


Position in Free Fall (cont.)5 meters

20 meters

45 m

Release1 second

2 seconds

3 s

4 seconds80 meters

Distance Fallen =[½ (Acceleration)(Time)](Time)

Galileo realized that:

Gravity acceleration is 10 meters per second per second, so at a time of 3 seconds,

Distance Fallen =½ (10m/s2)(3s)(3s) = 45 m

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Demo: Dropping the Ball

Distance Fallen = d = ½ at2

t2 = 2d/a = 2(3m)/(10 m/s2) = 0.6s2

t = √0.6s2 = 0.77 s

How long does it take a ball to fall 3 meters?Using the formula,

Beauty of science: Predict, then verify by dropping balls!


Demo: Catch a Buck

Put thumb and index fingers near Washington’s head. Can you react fast enough to catch the money?

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Demo: Reaction Time

Release

Catch

Distance (inch) Time (s)1 0.072 0.103 0.124 0.145 0.166 0.177 0.198 0.2010 0.2312 0.2514 0.2716 0.2918 0.30


Force & Acceleration

Newton’s First Law of Motion,

Zero Force Constant Velocity

Definition of Acceleration,

(Acceleration) = (Change in Velocity)

(Time interval)

implies

(same as uniform motion)

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Force Implies Acceleration

From those two results we have that,

Net Forcenot Zero

ObjectAccelerates

implies impliesVelocity

notConstant

So, if there’s a net force on an object, the object accelerates.Also, if an object accelerates, there must be a net force on it.


Acceleration Goes As Force

Larger the net force, greater the acceleration

Double the Force

Triple the Force

Half the Force

impliesDouble the Acceleration

Triple the Acceleration

Half the Acceleration

implies

implies

Acceleration “goes as” Force Force “goes as” Acceleration.

Mathematically, we write Force ~ Acceleration.

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Check YourselfYou push on a crate with 100

Newtons of force. If friction force is 100 Newtons, does the crate accelerate?

Does that mean that crate is not moving?

Now push with 150 N; friction is still 100 N. Does crate accelerate?

A friend helps push with an additional 150 N. By how much does acceleration increase?


Mass: Quantity of matter in an objectWeight: Force of gravity on an object

Mass is a universal property.Weight depends on gravity

(different on Moon).

Mass is the measure of inertia.SI unit for mass is the kilogram.SI unit for weight is Newton (since it’s a force)

Mass & Weight

Earth Moon

Weight

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More Mass, Less AccelerationThe greater the mass of an object, the less it

accelerates when acted on by same force.


Mass & AccelerationFor a given force, greater mass → smaller acceleration

Double the Mass

Triple the Mass

Half the Mass

impliesHalf the Acceleration

Third of the Acceleration

Double the Acceleration

implies

implies

Acceleration goes as the inverse of mass.

Mathematically, we write,Acceleration ~ 1/(Mass).

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Check Yourself

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?????

?????

?????

NOFRICTION


Newton’s Second Law of Motion

Acceleration goes as net Force.Acceleration goes as inverse of Mass.Acceleration only depends on Force and Mass.

Acceleration is in the direction of the net Force.

(Acceleration) = (Net Force)

(Mass)

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Newton’s Second Law of Motion

Or, more familiarly,

, and choosing appropriate units we can make F Fa am m

≈ =

This is the mathematical expression ofNewton’s 2nd Law of Motion.

Units: Mass has SI units of kg, and acceleration has SI units of m/s2. We define the SI unit of force as:1 newton = 1 N = 1kg m/s2.


Example: Accelerated Mass

A net force of 3.0 N produces an acceleration magnitude of 2.0 m/s2 on an object of unknown mass.

What is the mass of the object?

1 21

(3.0 N)= 1.5 kg(2.0 m/s )

Fma

= =

m1

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Newton’s Second Law of MotionAn object may have several forces acting on

it; the acceleration is due to the net force:


Practical Forces• Some contact forces

– Normal Force (Support Force) -- Already discussed– Friction– Drag (Fluid friction)– Spring Force– Tension force (ropes, etc.)

• Some non-contact forces– Gravitational force (Weight)– Electric force

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Weight & GravityThe falling box is pulled toward Earth by long-range force of gravity. The gravitational pull on an object on or near the surface of the Earth is called weight, for which we use the symbol W.Weight force is the entire Earth pulling on an object. Weight acts equally on objects at rest or in motion. The weight vector always points vertically downward, and it can be considered to act at the center of mass of the object.

W

W = mg g = 9.80 N/kg = 9.80 m/s2 down


Weight on EarthFrom Chap. 3, acceleration of gravity on Earth is about9.8 meters per second per second. (Notation: g = 9.8 m/s2 )

From Newton’s Second Law,

(Force) = (Mass) X (Acceleration)

For example, weight (force of gravity) for 1 kg is

( 9.8 Newtons ) = ( 1 kg ) X ( 9.8 m/s2 )

Can write g as 9.8 N/kg

1kg

9.8 N

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Free Fall AccelerationNewton’s Second Law explains why all

objects free fall with same acceleration.

Free Falla = F/m = mg/m = g

1 kg2 kg

a = (1kg)g/(1kg) = g a = (2kg)g/(2kg) = g


Newton’s Law of GravityNewton proposed that every object in the universe

attracts every other object with a force having following properties:

1. Force is inversely proportional to square of distance between objects.

2. Force is directly proportional to the product of the masses of the two objects.

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Newton’s Law of Gravity

1 21 on 2 2 on 1 2

m mF F Gr

= =

211 26.673 10 N m /kgG −= ×

r is distance between mass m1 and mass m2.

Direction of force on m1 is toward m2; direction of force on m2 is toward m1.


Apparent WeightYour perception of your weight is based on the support forces between your body and your surroundings. If your surroundings are accelerating, your apparent weight maybe more or less than your actual weight.

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Force felt from contact with the floor (or a scale, etc.) in an accelerating system.

Apparent Weight

Wa> mg

Wa=mg

Elevator accelerates up:

Elevator accelerates down:Wa< mg

Elevator not accelerating:


Example: Bowling Ball in a Bag

Carry 6 kg bowling ball in a grocery bag. How much weight does the bag support?

If I yank upwards, accelerating the ball by 5 m/s2, how much additional support force is required?

What is the new total support force?

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Support Force of Elevator Cable

Tension in elevator cable depends on acceleration

10 N

1 kg

Zero acceleration

15 N

1 kg

5 m/s2 upward( ½ g upward)

5 N

1 kg

0 N

1 kg

5 m/s2 downward( ½ g downward)

10 m/s2 downward(Free fall)


Friction and Air ResistanceFriction and air resistance are forces opposing motion.

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FrictionOrigin of friction is molecular interaction between

solid surfaces.

Friction is complicated.

Friction depends on support force and on properties of the surface.

Basic properties of friction first established by Leonardo da Vinci.


Air Resistance (Drag)Origin of drag is molecules of gas (or liquid) striking

a moving object.Drag force depends on:

•Size (area) of the object•Speed of the object

Larger the size or speed, larger the drag.Also depends on shape of object, density of gas or liquid, etc.

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Air Resistance on a Falling ObjectGravity force on an object (i.e., weight) is constant but air resistance depends on an object’s speed.

As a falling object gains speed, the resistance force gets larger so the net force decreases.

Net force is sum of:Weight (downward)Resistance force (upward)


Check YourselfGolf ball has more mass than a ping-pong

ball. Force of gravity is greater on: golf ball, ping-pong ball, or the same?

The two balls are the same size; when speeds are equal, drag force is greater on which ball?

Which ball falls faster (which has greater acceleration)?

GolfBall

PingpongBall

Drag

Weight

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Terminal SpeedSpeed of falling objects increases until drag force

balances weight. When forces balance, zero acceleration so constant velocity.

Speed for which air resistance balances weight called terminal speed.

High terminal speed

Low terminal speed(large area of chute)


Key Points of Lecture 4

Before next lecture, read Hewitt through Chap. 4, into 5

Homework Assignment #1 (first graded assignment) is due before 11:00 PM on Thursday, Sept. 2.

Homework Assignment #2 (second graded assignment) is due before 11:00 PM on Sunday, Sept. 5.

Quiz Friday (Chaps. 2 & 3)

• Velocity changes in free fall: v = gt• Position change in free fall: d = ½gt2

• Newton’s Second Law: a = F/m or F = ma• Weight• Gravitational Force• Apparent Weight• Friction• Air drag and terminal speed

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