18-aug-15 physics 1 (garcia) sjsu chapter 4 newton’s second law of motion how does an object move...

Apr 19, 2023 Physics 1 (Garcia) SJSU

Chapter 4 Newton’s Second Law

of Motion

How does an object move when a force acts on it?


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)


Force Implies Acceleration

From those two results we have that,

Net Forcenot Zero

ObjectAccelerates

implies impliesVelocity

not Constant

So if there’s a net force on an object, that implies that the object accelerates.Also have that if an object accelerates, that implies that there’s a net force.


More Force, More Acceleration

The greater the net force on an object, the greater the acceleration of that object.


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.


Check Yourself

You push on a crate with 100 Newtons of force. If the friction force is 100 Newtons, does the crate accelerate?

Does that mean that the crate is not moving?


Check Yourself (cont.)

Now push with 150 N; friction is still 100 N. Does the 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.Metric unit for mass is the kilogram.Metric unit for weight is Newton (since it’s a force)

Mass & Weight

Earth Moon

Weight


More Mass, Less Acceleration

The greater the mass of an object, the less it accelerates when acted on by a force.


Demo: Hammer Head

Hammer a nail into a piece of wood placed on top of massive object (gold brick or huge book).

Inertia of massive object keeps it from moving; can place on top of head and not feel it.


Mass & Acceleration

For a given force, greater mass, smaller the 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).


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)


Demo: Spool

Pull on string wrapped around a spool. Force is to the right. In what direction does the spool move?

Spool moves? Spool moves?

Pull Pull


Demo: Tricycle

Pull on tricycle pedal with a string.

Which direction does the tricycle move?

Bike moves? Bike moves?

PullPull

Pedal in top position Pedal in bottom position

http://www.physics.umd.edu/lecdem/services/demos/demosd1/d1-81.mpg


Weight on Earth

From the Chapter 3, acceleration of gravity on Earth is 10 meters per second per second. (Notation: g = 10 m/s2 )

From Newton’s Second Law,

(Force) = (Mass) X (Acceleration)

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

( 10 Newtons ) = ( 1 kg ) X ( 10 m/s2 )

1 kg

10 N


Demo: Bowling Ball in a Bag

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

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


Demo: 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)


Free Fall Acceleration

Newton’s Second Law explains why all objects fall with same acceleration.

Ratio of weight/mass always the same since weight depends on mass.

Analogy with ratio of circumference / diameter always equals pi (3.1415…).


Demo: Falling in a Vacuum

Feather falls slowly due to air resistance force.

If we remove the air (create a vacuum) then feather and coin fall with same acceleration.


Movie: Falling on the Moon


Demo: Drop the Sheet

A flat sheet of paper falls slowly because of air resistance.

What happens if we place it on top of a book, blocking the air from reaching it?

AirResistance

Weight


Friction and Air Resistance

Friction and air resistance are forces opposing motion.


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.


Air Resistance on a Falling Object

Gravity 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 (upward)


Check Yourself

Golf 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


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(better open the chute!)

Low terminal speed(large area of chute)


Demo: Drop the CatCats seem to have an uncanny ability to survive

falls from high places. For example, cats have been known to survive falls of up to 32 stories. By contrast, dogs rarely survive falls of more than six stories. Humans usually die when they fall from such heights.

From: www.animalhealthcare.ca

In a study of cats that had fallen from up to 32 stories, an interesting finding emerged: while the rate of injury in cats seemed to increase linearly depending on the length of the fall, after seven stories, the rate of injury seemed to level off! In other words, the survival rate and severity of injuries were no more severe in a cat that fell seven stories than in one that fell 32 and in some cases, injuries were even less!


Demo: Drop the Cat (cont.)After further study, the reasons for this discrepancy

became clear. When a person falls from a building, maximum speed or "terminal velocity" (120 mph) is reached after 32 stories. Cats, on the other hand, achieve terminal velocity at 60 mph after falling only five stories!

Until a cat reaches terminal velocity, it will experience acceleration and tend to reflexively extend its limbs, making it more susceptible to injuries. However, when a cat reaches terminal velocity, its vestibular system (i.e. the organs of balance) become less stimulated, causing the cat to relax. It will then orient its limbs more horizontally (splay-legged), thereby increasing air drag in much the same way a parachute does. In this posture, the force of impact also appears to become more evenly distributed.

18-aug-15 physics 1 (garcia) sjsu chapter 4 newton’s second law of motion how does an object move...

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