physics 1710 chapter 2 motion in one dimension

Physics 1710Physics 1710Chapter 2 Motion in One DimensionChapter 2 Motion in One Dimension

Cold Start-Quiz:Cold Start-Quiz:•What is the density of the Earth? What is the density of the Earth?

MM = 6 x 10 = 6 x 102424 kg kg

40 000 40 000 000 m000 m

V = C3 /8π2 = 1.x1021 m3

ρ = M/V = 6.x1024 kg/1.x1021 m3

ρ = 6.x103 kg/ m3

ρ = 6. kg/ liter = 6. g/ml

The earth is about six times more dense than the ocean.


Foolscap Quiz:Foolscap Quiz:•What is the volume of the Earth?What is the volume of the Earth?•What is the density of the Earth if What is the density of the Earth if its mass is its mass is

MM = 6 x 10 = 6 x 102424 kg? kg?

•(Use 1 significant figure.)(Use 1 significant figure.)40 000 40 000 000 m000 m


V = [4V = [4ππ/3]r /3]r 33 =2/3 (2 =2/3 (2ππ r ) r )33/ (2/ (2ππ ) )22 = 2/3 C = 2/3 C33/ (2/ (2ππ))22 = =

V = 0.7 V = 0.7 ••(4. X 10(4. X 10 7 7 ))33/ (2 / (2 • 3) • 3) 22 = = = 0.7 • 6 x 10 = 0.7 • 6 x 10 2222 /(4. X 10 /(4. X 10 1 1) =) =

= 1. X 10= 1. X 10 21 21 m m 3 3 = 1. X 10 = 1. X 10 18 18 liters liters

ρρ= M= M / V = 6 x 10 / V = 6 x 10 24 24 / 1. X 10 / 1. X 10 21 21 kg/ m kg/ m 3 3 = =

ρρ = 6 x 10 = 6 x 10 33 kg/ m kg/ m 3 3 = 6 kg/liter = 6 kg/liter


Galileo GalileiGalileo Galilei(1564-1642)(1564-1642)

• Pioneered kinematicsPioneered kinematics• Discredited AristotleDiscredited Aristotle• Discovered moons of JupiterDiscovered moons of Jupiter• Argued for Copernican Argued for Copernican UniverseUniverse


11′′ Lecture Lecture• Displacement Displacement is the is the changechange in in positionposition..

• VelocityVelocity is the time is the time raterate of of displacementdisplacement..

• AccelerationAcceleration is the time is the time raterate of of changechange in in velocityvelocity..


Displacement is the change in Displacement is the change in position.position.

ΔΔx =x = xxfinal final - x - xinitialinitial

ΔΔ is the change “operator”: is the change “operator”:

Change in Change in x =x = x at endx at end – x– x at startat start

ΔBalanceΔBalance = = BalanceBalancefinal final - - BalanceBalanceinitialinitial


Velocity is the Velocity is the time ratetime rate of of displacement.displacement.

Average velocity:Average velocity:vvx, ave x, ave = = ΔΔ x / x / ΔΔtt

Instantaneous velocity:Instantaneous velocity:vvx x = lim = lim ΔΔtt→∞→∞ ΔΔx /x / ΔΔt = t = dx/dtdx/dt


Posit

ion

(m

)

Time (sec)


VelocityVelocityP

osit

ion

(m

)

Time (sec)

vvx, ave x, ave = = ΔΔx / x / ΔΔtt

AverageAverageVelocityVelocity

vvx x = = dx/dtdx/dt

Instantaneous Instantaneous VelocityVelocity

ΔΔtt

ΔΔx x

Plot it!


Acceleration is the Acceleration is the time ratetime rate of of changechange of of velocity.velocity.

Average acceleration:Average acceleration:aax, ave x, ave = = ΔΔvvxx / / ΔΔt = (vt = (vx,final x,final -v-vx, initial x, initial )/ )/ ΔΔt t

Instantaneous acceleration:Instantaneous acceleration:aax x = lim = lim ΔΔtt→∞→∞ ΔΔvvxx / / ΔΔt = dvt = dvx x /dt/dt

aax x = dv= dvx x /dt =d(dx/dt =d(dxx x /dt)/dt = d/dt)/dt = d22x/dtx/dt 2 2


Motion MapMotion MapFrom “snap shots” of motion at From “snap shots” of motion at

equal intervals of time determine equal intervals of time determine the displacement, the average the displacement, the average

velocity and the average velocity and the average acceleration in each case.acceleration in each case.

Uniform motion

Accelerated motion

VelocityVelocity


Posit

ion

(m

)

Time (sec)

Plot them!

Velo

cit

y

(m/s

ec)

Time (sec)

a1= 0

a2>0

vvx x = = dx/dtdx/dt

aax x = = dvdvx x /dt/dt


Summary:Summary:The understanding of acceleration is the The understanding of acceleration is the key to understanding kinematics.key to understanding kinematics.

The acceleration of freely falling bodies The acceleration of freely falling bodies is is constantconstant..

physics 1710 chapter 2 motion in one dimension

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