Chapter 2a Motion

2-1. Speed 2-2. Vectors2-3. Acceleration2-4. Distance, Time, and Acceleration 2-5. Free Fall System2-6. Air Resistance2-8. Mass

2-9. 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• 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

mphhourmiles

hoursmiles

tdv 4040

5.2100

mileshourshourmilestvd 180630

hourshourmiles

mileshourmiles

milesvdt 5.2

/5.2

/40100

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. AccelerationAcceleration 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 timespeedin changeonAccelerati

tvva if

2-3. Acceleration3 Types of Acceleartion

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.

The Slinky ExperimentSuper Slinky Experiment

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 m½ (9.8)32 = 44.1 m½ (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.

2-6. 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

2-5. 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

2-7. 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 PendulumOther Web sites that illustrate the Foucault Pendulum.

http://en.wikipedia.org/wiki/File:Foucault-rotz.gifhttp://www.physclips.unsw.edu.au/jw/foucault_pendulum.htmlhttp://aspire.cosmic-ray.org/labs/scientific_method/pendulum.swfhttp://www.calacademy.org/products/pendulum/page7.htmhttp://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.

Balloon in car viedo

2-9. Second Law of MotionNewton'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 samegravity) 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 Motion833 N is needed to make this turn.

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

2-12. Circular Motion

http://www.youtube.com/watch?v=84L5uXOyVhwhttp://www.youtube.com/watch?v=TGHvFpNCrtQhttp://www.youtube.com/watch?v=6NAZtd-qHSQhttp://www.youtube.com/watch?v=A0H7TYzcMaY

2-13. Newton's Law of Gravity

221 force nalGravitatio

RmGmF

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 ) 6 106.67 10 /

GmMR

gR m s mM kgG 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 SatellitesThe 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.