Chapter 2 Motion

2-8. Mass2-9. Second Law of Motion2-10. Mass and Weight2-11. Third Law of Motion 2-12. Circular Motion2-13. Newton's Law of Gravity2-14. Artificial Satellites

2-1. Speed 2-2. Vectors2-3. Acceleration2-4. Distance, Time, and Acceleration 2-5. Free Fall System2-6. Air Resistance2-7. First Law of Motion

2-1. Speed• Definitions:

– Speed• The rate at which something moves a given distance.

• Faster speeds = greater distances

– General formula for speed:• Speed = distance / time

• Abbreviations commonly used:d = distance t = time v = speed

v = d/t

2-1. Speed

mphhour

miles

hours

miles

t

dv 4040

5.2

100

mileshourshour

milestvd 180630

hourshourmiles

miles

hourmiles

miles

v

dt 5.2

/5.2

/40

100

Velocity

Distance

Time

2-1. Speed

Average speed is the total distance traveled by an object divided by the time taken to travel that distance. 

Instantaneous speed is an object's speed at a given instant of time.

2-2. Vectors

Magnitude of a quantity tells how large the quantity is.

Scalar quantities have magnitude only.

Vector quantities have both magnitude and direction.

2-2. Vectors

Velocity is a vector quantity that includes both speed and direction.

2-3. Acceleration

Acceleration of an object is the rate of change of its velocity and is a vector quantity. For straight-line motion, average acceleration is the rate of change of speed:

interval time

speedin changeonAccelerati

t

vva

if

2-3. Acceleration

3 Types of Acceleration

Speeding Up

Slowing Down

Turning

2- 4. Distance, Time and Acceleration

(V1 + V2) Vavg =

2

d = vavg t

d = ½at2

(20mph + 60mph) = 40mph 2

30mph 2hr = 60miles

½ 10m/s/s 52 = 125m

2-5. Free Fall

The acceleration of gravity (g) for objects in free fall at the earth's surface is 9.8 m/s2.

Galileo found that all things fall at the same rate.

2-5. Free Fall

The rate of falling increases by 9.8 m/s every second.

Height = ½ gt2

For example:

½ (9.8 )12 = 4.9 m

½(9.8)22 = 19.6 m

½ (9.8)32 = 44.1 m

½ (9.8)42 = 78.4 m

2-5. Free Fall

A ball thrown horizontally

will fall at the same rate as a ball dropped

directly.

2-5. Free Fall

A ball thrown into the air will slow down, stop,

and then begin to fall with the acceleration

due to gravity. When it passes the thrower, it will be traveling at the same rate at which it

was thrown.

2-5. Free Fall

An object thrown upward at an angle to the ground follows a curved path called

a parabola.

2-6. Air Resistance

• In air…– A stone falls faster

than a feather• Air resistance

affects stone less

• In a vacuum– A stone and a

feather will fall at the same speed.

2-6. Air Resistance

• Free Fall– A person in free

fall reaches a terminal velocity of around 54 m/s

– With a parachute, terminal velocity is only 6.3 m/s

• Allows a safe landing

2-6. Air Resistance

• Ideal angle for a projectile– In a vacuum, maximum distance is at an angle of 45o

– With air resistance (real world), angle is less• Baseball will go furthest hit at an angle of around 40o

2-7. First Law of Motion

The first law of motion states: If no net force acts on it, an object at rest remains at rest and an object in motion remains in motion at a constant velocity.

Foucault PendulumInertia keeps a pendulum swinging in the same direction regardless of the motion of the earth. This can be used to measure the motion of the earth. As the Foucault Pendulum swings it appears to be rotating, but it is the earth that is rotating under it. To the right is the Foucault Pendulum at the Pantheon in Paris, France.

Foucault Pendulum

Other Web sites that illustrate the Foucault Pendulum.

http://en.wikipedia.org/wiki/File:Foucault-rotz.gif

http://www.physclips.unsw.edu.au/jw/foucault_pendulum.html

http://aspire.cosmic-ray.org/labs/scientific_method/pendulum.swf

http://www.calacademy.org/products/pendulum/page7.htm

http://www.youtube.com/watch?v=nB2SXLYwKkM

2-8. Mass

Inertia is the apparent resistance an object offers to any change in its state of rest or motion.

2-9. Second Law of Motion

Newton's second law of motion states: The net force on an object equals the product of the mass and the acceleration of the object. The direction of the force is the same as that of the acceleration.

F = Ma

2-9. Second Law of Motion

A force is any influence that can cause an object to be accelerated.

)(kg)(m/s 1 N 1 newton 1 2

The pound (lb) is the unit of force

in the British system of

measurement:

1 lb = 4.45 N (1 N = 0.225 lb)

2-10. Mass and Weight

• WeightDefinition: The force with which an object is

attracted by the earth’s gravitational pull• Example: A person weighing 160 lbs is being pulled

towards the earth with a force of 160 lbs (712 N).

– Near the earth’s surface, weight and mass are essentially the same

gravity) ofeleration (mass)(acc Weight

mgw

2-11. Third Law of Motion

The third law of motion states: When one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object.

2-11. Third Law of Motion

Examples of the 3rd Law

2-12. Circular Motion

Centripetal force is the inward force exerted on an object to keep it moving in a curved path. Centrifugal force is the outward force exerted on the object that makes it want to fly off into space.

2-12. Circular Motion

2-12. Circular Motion

833 N is needed to make this turn.

If he goes too fast, which wheels are likely to come off the ground first?

2-13. Newton's Law of Gravity

221 force nalGravitatio

R

mGmF

G = 6.67 x 10-

11 N•m/kg2

2-13. Newton's Law of Gravity

• How can we determine the mass of the earth using an apple?– This illustrates the way

scientists can use indirect methods to perform seemingly “impossible tasks”

2-13. Newton's Law of Gravity

• How can we determine the mass of the earth using an apple?– This illustrates the way scientists can use

indirect methods to perform seemingly “impossible tasks”

2

2 2 6 224

11 2 2

Gravitational force on apple F

(9.8 / )(6.4 10 )6 10

6.67 10 /

GmM

R

gR m s mM kg

G N m kg

= mg

2-15. Artificial Satellites

• The world's first artificial satellite was Sputnik I, launched in 1957 by the Soviet Union.

GPS-Global Positioning Satellite

2-15. Artificial Satellites

The escape speed is the speed required by an object to leave the gravitational influence of an astronomical body; for earth this speed is about 40,000 km/h.

2-15. Artificial Satellites

The escape speed is the speed required by an object to leave the gravitational influence of an astronomical body; for earth this speed is about 40,000 km/h.

Rotation & Revolution Axis

A straight line through which circular motion takes place

All points on object orbit around the axis All rotation/revolution requires an axis

Rotation & Revolution

Rotation Object rotating about an internal axis Ex. Daily motion of the Earth, spiral football

Revolution Object rotating about an external axis Ex. Yearly motion of the earth

How do we describe how fast something is rotating??

Speeds for objects in a straight line are called linear (or tangential) speeds, Linear speeds are a rate at which an object

covers a certain distance (v =d/t) Ex. Unit – m/s , km/hr , mph

Can’t express speeds of rotation with a linear speed, b/c objects at different points on the rotating

object have different linear speeds

Rotational speed Expresses the rate at which an object rotates

through a portion of a circle ( an angle) Ex. Unit --- RPM’s

Below, a record spinning on a axis through its center (black dot)

Faster linear speed, Star or Smiley??Smiley, travels a greater distance for eachFull spin.

Faster rotational speed, Star or smiley?? Both the same, b/c entire record is rotating at the same rate

Are all people on Earth moving at the same speed??

Earth is rotating about an axis through its poles

So that means we are all moving since we are all on the Earth.

Are some of us moving with a greater LINEAR SPEED than others?? Yes, closer to the Equator, the faster you are

moving…. Closer to poles, the slower you are moving

Are some of us moving with a greater ROTATIONAL SPEED than others?? No, all people on earth have same rotational

speed, because Earth is spinning at the same rate everywhere

Centripetal Acceleration

• Tangential speed (vt) depends on distance

• When tangential speed is constant, motion is described as uniform circular motion

• An object moving in a circle at a constant speed still has an acceleration due to its change in direction

• Velocity is a vector so acceleration can be produced by a change in magnitude and direction

• Centripetal Acceleration is acceleration caused by a change in direction, directed toward the center of a circular path

• ac = Vt2 / r

Centripetal Acceleration

Centripetal Force When driving in a circle, in what direction

is a force acting on you? Pushing you outward from the circle, or

inward? If you are swinging a yo-yo in a circle, and the

string breaks…. What path does the yo – yo take??

Ans. -- Inwards, toward the center of the circle

Ans -- yo- yo goes in a path tangent to the circle

?

Centripetal Force

HOWEVER, People commonly think there is a force pushing you out from the circle Feels like you are being pushed outward Example ….. The Rotor- amusement park

ride, a centrifuge, CD on your dashboard moving to the right when your turning left

Why is this??

The RotorPeople Stand with backs against wall of a large cylinder, cylinder then starts spinning,

and people are seemingly pushed

against the wall, then floor drops, and people are stuck against the

wall.

http://www.youtube.com/

watch?v=uz_DkRs92pM

So why is there no Force pushing you out from the circle??

A force does not cause this…… your INERTIA does!!

Inertia makes you want to stay in a straight line, and by going in a circle, you are fighting your own inertia This is how Rotor works, and why CD on

dashboard happens

The only actual force acting on you is the

Centripetal Force

Centripetal Force Centripetal means “center-

Seeking” Force pushes you toward the

center of the circle Is the force that keeps you moving in a circle, and keeps your inertia from taking you in a straight line

Centripetal Force is affected by.. Mass (m),

linear speed (vt), and radius (r)

Centripetal Force• Inertia wants to take objects in a tangent line,

to the circular path

• Inertia is why you feel like your being pushed outward– This outward pushing is sometimes called the

Centrifugal Force• but it is not actually a force, is only inertia

• Every object that moves in circular motion must experience a centripetal force from somewhere