chapter 2 motion
DESCRIPTION
Chapter 2 Motion. 2-1. Speed 2-2. Vectors 2-3. Acceleration 2-4. Distance, Time, and Acceleration 2-5. Free Fall System 2-6. Air Resistance 2-7. First Law of Motion. 2-8. Mass 2-9. Second Law of Motion 2-10. Mass and Weight 2-11. Third Law of Motion 2-12. Circular Motion - PowerPoint PPT PresentationTRANSCRIPT
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