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Mechanics & Molecular Kinetic Theory. Contents. Mechanics Molecular Kinetic Theory. Mechanics. Linear Motion : speed (m/s) = distance (m) time(s) velocity (m/s) = displacement (m) time (s) acceleration (m/s 2 ) = change in speed (m/s) time taken (s). - PowerPoint PPT Presentation
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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 gravitygravitye.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 = speed)(d/t = 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 GasesRobert 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)
MolesMolesIn the periodic table:Oxygen = O Carbon = C Helium = He8
166
1224
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 gasIf 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 gasIf the gas is compressed:volume decreases, temperature decreasesSo 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 gasIf the gas is heated:temperature increases, pressure increasesSo keeping everything else constant:p/T = constant or p α T
p
T (K)0
Ideal Gas EquationIdeal Gas EquationThe 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 earlierpV = nRTpV = nRT
where 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