PhysicsDr. A. Búcsi room No O-3

bucsi@fpharm.uniba.sk

Physics –

Exam (test) 80%

Exercises 20%

Minimum requirement 60%

Problem solving

• Physics - measurable quantities

- units

International System of Units (Le Système Internationald'Unités) – SI

Seven dimensionally independent,

fundamental,

irreducible

and complete system

• meter - unit of length

• 1 m is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

• The current definition had the effect of fixing the speed of light in a vacuum at exactly 299 792 458 m/s.

• History – derived using the distance of the North pole from the Equator, later length of a platinum-iridium bar

m

• kilogram - unit of mass

• The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

• platinum-iridium cylinder -the international prototype of the kilogram

kg

• second – unit of time

• Duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

• History - the fraction 1/86 400 of the mean solar day

E=h f𝜆 = 𝑐 /𝑓

s

• Ampere – unit of electric current

• The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7

newton per meter of length.

A

• Kelvin – unit of thermodynamic temperature

• The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Celsius temperature is the degree Celsius - °C, which is by definition equal in magnitude to the kelvin

t/°C = T/K - 273.15.

• degree Kelvin

K

• mole – unit of the amount of substance

• The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. (NA=6.022x1023 Avogadro’s number)

• elementary entities - atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

mol

• candela – luminous intensity

• luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

cd

Derived units.

radian 0-2 π [rad] = (m/m)=1

Arc length 𝑙 = 𝛼 𝑟 [α]=rad

circumference= 2π radius

steradian (square radian) 0-4 π

[sr] = (m2 /m2)=1

Surface area S = 𝛽𝑟2 [β]=sr

sphere surface area = 4 π radius2

degree Celsius

t [°C] = T – 273.15 [K]

Multiplication and/or division of fundamental units

Examples

Speed: length/time -> [v] = m/sAcceleration: speed/time -> [a] = m/s2

Force: mass x acceleration -> [F]= kg m/s2 = NPressure: force/area => [P] = N / m2 = kg /ms2

= Paetc…

Multiplicaton factors

Conversion of units

• Example1 v= 28 m/s ? km/h

28𝑚

𝑠

1𝑘𝑚

1000𝑚

3600𝑠

1ℎ= 28

3600

1000ൗ𝑘𝑚ℎ

28 Τ𝑚𝑠 = 100.8 ൗ𝑘𝑚

ℎ

• Example2 κ=3400 μS cm-1 ? S m-1

3400 𝜇𝑆𝑐𝑚 −11𝑆

106𝜇𝑆

100 𝑐𝑚

1𝑚= 0.34𝑆𝑚−1

Scalars and vectorsScalars - magnitude

Temperature, speed, mass, volume...

Vectors – magnitude, direction and orientation.

force, displacement, velocity, acceleration...

Vector notation

Vector equality

Vector representation –a=(x,y,z)a=(r,θ,ϕ)

Components(2D)

• Vector operations

Addition

Graphical

• Calculation

• Subtraction

B(Bx,By) => - B(-Bx,-By)

A – B = A + (-B)

𝐴 + 𝐵

= 𝐴 2

+ 𝐵 2

+ 2 𝐴 𝐵 𝑐𝑜𝑠𝜃

0 4 8 12 160

7

14

21

28

3 A (15,21)

y

x

A (5,7)parallel

Multiplication with scalarA (Ax,Ay)

k A = (kAx,kAy)

result - vector

• Scalar (dot) product of two vectors

result – scalar !!

𝐷 = 𝐴 ∙ 𝐵 cos 𝜃

𝐷 = 𝐴𝑥𝐵𝑥 + 𝐴𝑦𝐵𝑦

• Vector product of two vectors

Magnitude

|A x B| = |A| |B| sinθ

A x B = ‒ B x A

Result – vector!!

A x B (AyBz-AzBy, AxBz-AzBx, AxBy-AyBx)

Newtonian MechanicsKinematics, dynamics

Masspoint mechanics

• Dimensionless object with mass – point

trajectory - s (d,h) [m]speed – velocity v (u) [m/s]acceleration a [m/s2]time t [s]

Uniform linear motion

• Trajectory – along straight line

• Speed – constant

• Acceleration - zero

s = s0 + v0 . t

v = v0 = const.

a = 0

v0= (s-s0)/t

𝑣 = න 𝑎 𝑑𝑡 = 0 + 𝑐𝑜𝑛𝑠𝑡

𝑠 = න 𝑣0𝑑𝑡 = 𝑣0𝑡 + 𝑐𝑜𝑛𝑠𝑡

Uniformly accelerated linear motion

a=constant

a = const.

𝑡 = 0 ⟹ 𝑣 = 𝑣0

𝑡 = 0 ⟹ 𝑠 = 𝑠0

𝑣 = න 𝑎 𝑑𝑡 = 𝑎𝑡 + 𝑣0

𝑠 = න 𝑣 𝑑𝑡 = න 𝑎𝑡 + 𝑣0 𝑑𝑡 =1

2𝑎𝑡2 + 𝑣0𝑡 + 𝑠0

• Freefall – special case

standard acceleration due

to gravity - standard gravity

(Earth)

a=g=9,81 m/s2

𝑡 =2ℎ

𝑔

Summary

SI units

Vectors 𝐴 + 𝐵 = 𝐴 2

+ 𝐵 2

+ 2 𝐴 𝐵 𝑐𝑜𝑠𝜃

𝐴 + 𝐵 = 𝐴𝑥 + 𝐵𝑥 , 𝐴𝑦 + 𝐵𝑦 tan 𝜃 =𝐴𝑦 +𝐵𝑦

𝐴𝑥 +𝐵𝑥

𝑘𝐴 = (𝑘𝐴𝑥 , 𝑘𝐴𝑦 )

𝐷 = 𝐴 𝐵 𝑐𝑜𝑠𝜃 𝐷 = 𝐴𝑥𝐵𝑥 + 𝐴𝑦𝐵𝑦

𝐴 𝑥𝐵 = 𝐴 𝐵 𝑠𝑖𝑛𝜃 𝐴 𝑥𝐵 = −𝐵 𝑥𝐴

Uniform linear motion

𝑠 = 𝑠0 + 𝑣0𝑡 𝑣 =Δ𝑠

Δ𝑡

Uniformly accelerated linear motion

𝑠 = 𝑠0 + 𝑣0𝑡 + 12ൗ 𝑎𝑡2 𝑣 =

𝑑𝑠

𝑑𝑡= 𝑣0 + 𝑎𝑡 𝑎 =

𝑑2𝑠

𝑑𝑡 2 =𝑑𝑣

𝑑𝑡

Freefall ℎ = 12ൗ 𝑔𝑡2