Theories and ExperimentsTheories and Experiments

The goal of physics is to develop theories The goal of physics is to develop theories based on experimentsbased on experiments

A theory is a “guess,” expressed A theory is a “guess,” expressed mathematically, about how a system mathematically, about how a system worksworks

The theory makes predictions about how a The theory makes predictions about how a system should worksystem should work

Experiments check the theories’ Experiments check the theories’ predictionspredictions

Every theory is a work in progressEvery theory is a work in progress

UnitsUnits

To communicate the result of a To communicate the result of a measurement for a quantity, a measurement for a quantity, a unit unit must be definedmust be defined

Defining units allows everyone to Defining units allows everyone to relate to the same fundamental relate to the same fundamental amountamount

Systems of MeasurementSystems of Measurement

Standardized systemsStandardized systems• agreed upon by some authority, usually agreed upon by some authority, usually

a governmental bodya governmental body SI -- SystSI -- Systééme Internationalme International

• agreed to in 1960 by an international agreed to in 1960 by an international committeecommittee

• main system used in this textmain system used in this text• also called mks for the first letters in the also called mks for the first letters in the

units of the fundamental quantitiesunits of the fundamental quantities

TimeTime

UnitsUnits• seconds, sseconds, s

Defined in terms of the oscillation of Defined in terms of the oscillation of radiation from a cesium atomradiation from a cesium atom

US “Official” Atomic ClockUS “Official” Atomic Clock

LengthLength

UnitsUnits• SI – meter, mSI – meter, m• US Customary – foot, ftUS Customary – foot, ft

Defined in terms of a meter – the Defined in terms of a meter – the distance traveled by light in a distance traveled by light in a vacuum during a given timevacuum during a given time

MassMass

UnitsUnits• SI – kilogram, kgSI – kilogram, kg

Defined in terms of kilogram, based Defined in terms of kilogram, based on a specific cylinder kept at the on a specific cylinder kept at the International Bureau of Weights and International Bureau of Weights and MeasuresMeasures

Standard KilogramStandard Kilogram

MultipliersMultipliers

Prefixes correspond to powers of 10Prefixes correspond to powers of 10 Each prefix has a specific nameEach prefix has a specific name Each prefix has a specific Each prefix has a specific

abbreviationabbreviation Larger: kilo(k), Mega (M), etcLarger: kilo(k), Mega (M), etc Small: milli (m), micro(Small: milli (m), micro(), nano(n)), nano(n)

SpeedSpeed

The The average speedaverage speed of an object is of an object is defined as the total distance traveled defined as the total distance traveled divided by the total time elapseddivided by the total time elapsed

The total distance and the total time The total distance and the total time are all that is importantare all that is important

SI units are m/sSI units are m/s

t

xv

Speed, contSpeed, cont

Average speed totally ignores any Average speed totally ignores any variations in the object’s actual variations in the object’s actual motion during the tripmotion during the trip

The total distance and the total time The total distance and the total time are all that is importantare all that is important

SI units are m/sSI units are m/s

ExampleExample

Car travels 350 km in 7 hours. What is Car travels 350 km in 7 hours. What is its speed?its speed?

SpeedSpeed

Instant Speed v: speed at any Instant Speed v: speed at any particular instantparticular instant

Constant Speed: Speed v does not Constant Speed: Speed v does not change during motionchange during motion

2 hours at 75km/h

1h at 50km/h, then 1h at 100km/h

Same average speed

VelocityVelocity

Both speed and direction of motion are Both speed and direction of motion are specifiedspecified

Represented by a Represented by a Vector Vector quantityquantity Magnitude (speed)Magnitude (speed) DirectionDirection graphgraph

Vector: velocity, force, electric field

Scalars:speed, temperature, time, energy

Acceleration(a)Acceleration(a)

Time rate of change of the velocity Time rate of change of the velocity

Units m/s² (SI)Units m/s² (SI) Instant acceleration: at any particular Instant acceleration: at any particular

instantinstant Constant acceleration: same at any instantConstant acceleration: same at any instant graphgraph

t

vva

o

Average AccelerationAverage Acceleration

Vector quantityVector quantity When the sign of the velocity and the When the sign of the velocity and the

acceleration are the same (either acceleration are the same (either positive or negative), then the speed positive or negative), then the speed is increasingis increasing

When the sign of the velocity and the When the sign of the velocity and the acceleration are in the opposite acceleration are in the opposite directions, the speed is decreasingdirections, the speed is decreasing

Linear motion (one dimension)Linear motion (one dimension)

Constant velocity v: x= vtConstant velocity v: x= vt Constant acceleration a: Constant acceleration a:

t

vva

o

2

2

1attvx o

Linear Motion SummaryLinear Motion Summary

(1)(1)

(2)(2)

(3)(3)

(4) (4)

t

vva

o

2

2

1attvxx oo

tvv

xxo

o2

)(2

22

o

o

xx

vva

ExampleExample

An antelope moving with constant An antelope moving with constant acceleration covers the distance acceleration covers the distance between two points A and B, 60 m between two points A and B, 60 m apart in 6 s. Its velocity as it passes apart in 6 s. Its velocity as it passes the second point is 15 m/s. What is the second point is 15 m/s. What is the acceleration? What is the velocity the acceleration? What is the velocity at point A?at point A?

Problem 1Problem 1

A speedboat increases its speed at a A speedboat increases its speed at a constant rate of 2m/ s².constant rate of 2m/ s².

a.a. How much time is required for the How much time is required for the speed to increase from 8m/s to speed to increase from 8m/s to 20m/s20m/s

b.b. How far the boat travel during this How far the boat travel during this timetime

c.c. Average speedAverage speed

Galileo GalileiGalileo Galilei

1564 - 16421564 - 1642 Galileo formulated the Galileo formulated the

laws that govern the laws that govern the motion of objects in motion of objects in free fallfree fall

Also looked at:Also looked at:• Inclined planesInclined planes• Relative motionRelative motion• ThermometersThermometers• PendulumPendulum

Free FallFree Fall

All objects moving under the influence of All objects moving under the influence of gravity only are said to be in free fallgravity only are said to be in free fall• Free fall does not depend on the object’s Free fall does not depend on the object’s

original motionoriginal motion All objects falling near the earth’s surface All objects falling near the earth’s surface

fall with a constant accelerationfall with a constant acceleration The acceleration is called the acceleration The acceleration is called the acceleration

due to gravity, and indicated by due to gravity, and indicated by gg

Acceleration due to GravityAcceleration due to Gravity

Symbolized by Symbolized by gg gg = 9.80 m/s² = 9.80 m/s²

• When estimating, use When estimating, use gg 10 m/s10 m/s22

acc is always directed downwardacc is always directed downward• toward the center of the earthtoward the center of the earth

Ignoring air resistance and assuming Ignoring air resistance and assuming gg doesn’t vary with altitude over doesn’t vary with altitude over short vertical distances, free fall is short vertical distances, free fall is constantly accelerated motionconstantly accelerated motion

Free Fall – an object droppedFree Fall – an object dropped

Initial velocity is Initial velocity is zerozero

Let up be positiveLet up be positive Use the equationsUse the equations

• Generally use y Generally use y instead of x since instead of x since verticalvertical

Acceleration is Acceleration is gg = = 9.80 m/s9.80 m/s22

vo= 0

a = - g

Free Fall – an object thrown Free Fall – an object thrown downwarddownward

a = -9.80 m/sa = -9.80 m/s22

Initial velocity Initial velocity 0 0• With upward being With upward being

positive, initial positive, initial velocity will be velocity will be negativenegative

Free Fall -- object thrown Free Fall -- object thrown upwardupward

Initial velocity is Initial velocity is upward, so positiveupward, so positive

The instantaneous The instantaneous velocity at the velocity at the maximum height is maximum height is zerozero

a = - 9.80 m/sa = - 9.80 m/s22 everywhere in the everywhere in the motionmotion

v = 0

Thrown upward, cont.Thrown upward, cont.

The motion may be symmetricalThe motion may be symmetrical• Then tThen tupup = t = tdowndown

• Then v = -vThen v = -voo

The motion may not be symmetricalThe motion may not be symmetrical• Break the motion into various partsBreak the motion into various parts

Generally up and downGenerally up and down

Non-symmetrical Non-symmetrical Free FallFree Fall

Need to divide the Need to divide the motion into motion into segmentssegments

Possibilities includePossibilities include• Upward and Upward and

downward portionsdownward portions• The symmetrical The symmetrical

portion back to the portion back to the release point and then release point and then the non-symmetrical the non-symmetrical portionportion

Example of falling objectExample of falling object

y-axis points upy-axis points up vvo = o = 15 m/s15 m/s After 1sAfter 1s After 4sAfter 4s Maximum heightMaximum height Time to reach maximum heightTime to reach maximum height Velocity 6m above starting pointVelocity 6m above starting point

Falling object motion exampleFalling object motion example

A ball is thrown vertically down from a A ball is thrown vertically down from a 100 m tall building with a speed of 100 m tall building with a speed of 10m/s.10m/s.

How long will it take for the ball to How long will it take for the ball to reach ground?reach ground?

What is the velocity of the ball just What is the velocity of the ball just before hitting the ground?before hitting the ground?

What is the acceleration?What is the acceleration?