Mechanics &Mechanics &Molecular Kinetic TheoryMolecular Kinetic Theory

ContentsContents

MechanicsMechanics Molecular Kinetic TheoryMolecular Kinetic Theory

MechanicsMechanics

Linear MotionLinear Motion::

speed (m/s) = speed (m/s) = distance (m)distance (m)                 

time(s)time(s)

velocity (m/s) = velocity (m/s) = displacement (m)displacement (m)

time (s)time (s)

acceleration (m/sacceleration (m/s22) = ) = change in speed change in speed (m/s)(m/s)

time taken (s)time taken (s)

MechanicsMechanics

Distance vs. Time graphDistance vs. Time graph::

MechanicsMechanics

Speed vs. Time graphSpeed vs. Time graph::

MechanicsMechanics

Forces and VectorsForces and Vectors::

Examples:Examples:

- scalar = speed- scalar = speed (1 quantity… no direction)(1 quantity… no direction)

- vector = velocity- vector = velocity (2 quantities… speed & (2 quantities… speed & direction)direction)

Other vector quantities:Other vector quantities:

- displacement- displacement

- momentum- momentum

- force- force

Vectors can be added to produce a Vectors can be added to produce a resultantresultant quantity quantity

MechanicsMechanics

Adding vectors:Adding vectors:

And again…And again…

And again…And again…

+ =

- =

MechanicsMechanics

Angular mechanics:Angular mechanics:

Fx = F cos Fx = F cos Fy = F sin Fy = F sin

• Weight always faces downwards• Force on road is perpendicular to motion

MechanicsMechanics ProjectilesProjectiles::

- an object upon which the only force acting is - an object upon which the only force acting is gravitygravity

e.g. bullete.g. bullet

- once projected, its motion depends on its inertia- once projected, its motion depends on its inertia

Initial velocity vectors:Vx = Vcos VVyy = Vsin = Vsin

Flight timeFlight time::t = Vt = Viyiy/g/g

DisplacementDisplacement::X = VX = Vxxtt

Max. heightMax. height::Y = VY = Viyiyt + ½gtt + ½gt22

MechanicsMechanics MomentsMoments: have a direction (clockwise or anti-clockwise): have a direction (clockwise or anti-clockwise)

Moment = force × perpendicular distanceMoment = force × perpendicular distance (Nm) =(Nm) = (N) (N) x x (m)(m) clockwise moment = anti-clockwise moment (equilibrium)clockwise moment = anti-clockwise moment (equilibrium)

- this is used to find the centre of gravity- this is used to find the centre of gravity

Work = Force × distance moved in the direction of the Work = Force × distance moved in the direction of the forceforce

(Nm or J) = (N)(Nm or J) = (N) xx (m)(m)

- When work is done, energy is transferred- When work is done, energy is transferred- Energy comes in many forms; some kinds of energy can - Energy comes in many forms; some kinds of energy can be stored, while others cannotbe stored, while others cannot- Energy is - Energy is alwaysalways conserved conserved

MechanicsMechanics Power: rate at which energy is transferredPower: rate at which energy is transferred

power (W) = energy (J) / time (secs)power (W) = energy (J) / time (secs)

energy (work done) = force x distanceenergy (work done) = force x distance

So…So…

power = (force x distance) / timepower = (force x distance) / time (d/t = (d/t = speed)speed)

power = force x speedpower = force x speed

P = FvP = Fv

MechanicsMechanics EnergyEnergy: the ability to do work. When work is done, : the ability to do work. When work is done,

energy is transferredenergy is transferred

- Some kinds of energy can be stored, while others - Some kinds of energy can be stored, while others cannotcannot

- Energy in a system is always conserved- Energy in a system is always conserved

Potential EnergyPotential Energy::

potential energy = weight × distance moved against potential energy = weight × distance moved against gravitygravity

(Nm)(Nm) = (N) = (N) x x (m)(m)

Kinetic EnergyKinetic Energy::

kinetic energy = ½ mass x velocitykinetic energy = ½ mass x velocity22

(J)(J) = = (kg) x (m/s (kg) x (m/s22))

Heat CapacityHeat Capacity Heat capacity (c): quantity of heat required to raise Heat capacity (c): quantity of heat required to raise

the temperature of a unit mass by 1the temperature of a unit mass by 1°K°K

Heat flow =Heat flow = m m ×× c c × delta T× delta T(J)(J) = (kg) = (kg) × (Jkg× (Jkg-1-1KK-1-1)) × (K)× (K)

Q = mc delta Q = mc delta

specific latent heat: energy to change the state of a specific latent heat: energy to change the state of a unit mass of liquid without a temperature changeunit mass of liquid without a temperature change- fusion, or melting - fusion, or melting - vaporisation, or boiling- vaporisation, or boiling

delta Q = mldelta Q = ml

Newton’s LawsNewton’s Laws Newton’s 1Newton’s 1stst Law Law: : An object continues in its state of An object continues in its state of

rest or uniform motion in a straight line, unless it has rest or uniform motion in a straight line, unless it has an external force acting on itan external force acting on it

Newton’s 2Newton’s 2ndnd Law Law: : Rate of change of momentum is Rate of change of momentum is proportional to the total force acting on a body, and proportional to the total force acting on a body, and occurs in the direction of the forceoccurs in the direction of the force

F = maF = ma

Newton’s 3Newton’s 3rdrd Law Law: : If body A exerts a force on body B, If body A exerts a force on body B, body B must exert an equal and opposite force on body B must exert an equal and opposite force on body Abody A

CollisionsCollisions Conservation of MomentumConservation of Momentum: : Total momentum before Total momentum before

= total momentum after = total momentum after

MuMu11 + mu + mu22 = Mv = Mv11 + mv + mv22

Conservation of EnergyConservation of Energy: : Total energy before = total Total energy before = total energy after energy after

½Mu½Mu1122 + ½mu + ½mu22

22 = ½Mv = ½Mv1122 + ½mv + ½mv22

22

Elastic collisions: zero energy lossElastic collisions: zero energy loss

Impulse = Force x timeImpulse = Force x time (Ns) =(Ns) = (N) x (secs) (N) x (secs)

Ideal GasesIdeal Gases

Robert Brown investigated the movement of gas particles – 1820s

• Air particles (O2 and N2) – too small• Observe the motion of smoke grains

Smoke grain(speck of reflected light)

Light

Microscope

Glass box

Ideal GasesIdeal Gases

Smoke grain(speck of reflected light)

Light

Microscope

Glass box

Pick 1 grain & follow its movement- Jerky, erratic movement due to collisions with (the smaller) air molecules

Ideal GasesIdeal GasesSTP = standard temperature and pressure

T = 273K, p = 1 atmAverage speed of air molecules = 400ms-1

Pressure - in terms of movement of particles

• Air molecule bounces around inside, colliding with the various surfaces

• Each collision exerts pressure on the box

If we have a box filled with gas:If we have a box filled with gas:We can measure:We can measure: Pressure (NmPressure (Nm-2-2)) Temperature (K)Temperature (K) Volume (mVolume (m33)) Mass (kg)Mass (kg)

MolesMoles

In the periodic table:

Oxygen = O Carbon = C Helium = He8

16

6

12

24

Mass number = bottom number = molar mass

12 416

• Mass number = mass (g) of 1 mole of that substance• 6.02x1023 particles in 1 mole• e.g. 1 mole of He has a mass of 4 grams 1 mole of O2 has a mass of 32 grams

Mass (g) = number of moles x molar mass

Boyle’s LawBoyle’s Law Relates pressure & volume of the gasRelates pressure & volume of the gas

If the gas is compressed:volume decreases, pressure increases

So keeping everything else constant:pV = constant or p α 1/V

p p

V 1/V

Charles’ LawCharles’ Law Relates temperature & volume of the gasRelates temperature & volume of the gas

If the gas is compressed:volume decreases, temperature decreases

So keeping everything else constant:V/T = constant or V α T

V

T (C)

T (K)0 100 200 300 400

-300 -200 -100 0 100

Pressure LawPressure Law Relates temperature & pressure of the gasRelates temperature & pressure of the gas

If the gas is heated:temperature increases, pressure increases

So keeping everything else constant:p/T = constant or p α T

p

T (K)0

Ideal Gas EquationIdeal Gas Equation

The 3 gas laws can be written as a single equationThe 3 gas laws can be written as a single equation

which relates the 4 properties mentioned earlierwhich relates the 4 properties mentioned earlier

pV = nRTpV = nRTwhere R = universal gas constant = 8.31Jmolwhere R = universal gas constant = 8.31Jmol-1-1KK-1-1

n, number of moles = mass (g) / molar mass (g mol-1)

e.g. how many moles are there in 1.6kg of oxygen?molar mass of O2 = 32gmol-1

number of moles, n = 1600g/32gmol-1

= 50 mol

SummarySummary

VectorsVectors ProjectilesProjectiles MomentsMoments Power, Energy & WorkPower, Energy & Work Energy ChangesEnergy Changes Heat CapacityHeat Capacity Newton’s 3 LawsNewton’s 3 Laws CollisionsCollisions Molecular Kinetic TheoryMolecular Kinetic Theory