Download Mechanics & Molecular Kinetic Theory

Mechanics &
Molecular Kinetic Theory
Contents
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
Mechanics
Molecular Kinetic Theory
Mechanics
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Linear Motion:
speed (m/s) = distance (m)
time(s)
velocity (m/s) = displacement (m)
time (s)
acceleration (m/s2) = change in speed (m/s)
time taken (s)
Mechanics
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Distance vs. Time graph:
Mechanics
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Speed vs. Time graph:
Mechanics
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Forces and Vectors:
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Examples:
- scalar = speed
- vector = velocity
(1 quantity… no direction)
(2 quantities… speed & direction)
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Other vector quantities:
- displacement
- momentum
- force
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Vectors can be added to produce a resultant quantity
Mechanics
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Adding vectors:

And again…
=
+
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And again…
-
=
Mechanics

Angular mechanics:
Fx = F cos 
Fy = F sin 
• Weight always faces
downwards
• Force on road is
perpendicular to motion
Mechanics

Projectiles:
- an object upon which the only force acting is gravity
e.g. bullet
- once projected, its motion depends on its inertia
Initial velocity vectors:
Vx = Vcos  Vy = Vsin 
Flight time:
t = Viy/g
Displacement:
X = Vxt
Max. height:
Y = Viyt + ½gt2
Mechanics
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Moments: have a direction (clockwise or anti-clockwise)
Moment = force × perpendicular distance
(Nm) = (N)
x
(m)
clockwise moment = anti-clockwise moment (equilibrium)
- this is used to find the centre of gravity
Work = Force × distance moved in the direction of the force
(Nm or J) = (N)
x
(m)
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- When work is done, energy is transferred
- Energy comes in many forms; some kinds of energy can be
stored, while others cannot
- Energy is always conserved
Mechanics

Power: rate at which energy is transferred
power (W) = energy (J) / time (secs)
energy (work done) = force x distance
So…
power = (force x distance) / time
power = force x speed
P = Fv
(d/t = speed)
Mechanics

Energy: the ability to do work. When work is done, energy is
transferred
- Some kinds of energy can be stored, while others cannot
- Energy in a system is always conserved
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Potential Energy:
potential energy = weight × distance moved against gravity
(Nm)
= (N) x
(m)
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Kinetic Energy:
kinetic energy = ½ mass x velocity2
(J)
=
(kg) x (m/s2)
Heat Capacity

Heat capacity (c): quantity of heat required to raise the
temperature of a unit mass by 1°K
Heat flow = m
(J)
= (kg)
×
c
× delta T
× (Jkg-1K-1) × (K)
Q = mc delta 

specific latent heat: energy to change the state of a unit
mass of liquid without a temperature change
- fusion, or melting
- vaporisation, or boiling
delta Q = ml
Newton’s Laws

Newton’s 1st Law: An object continues in its state of rest or
uniform motion in a straight line, unless it has an external
force acting on it
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Newton’s 2nd Law: Rate of change of momentum is
proportional to the total force acting on a body, and occurs in
the direction of the force
F = ma
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Newton’s 3rd Law: If body A exerts a force on body B, body B
must exert an equal and opposite force on body A
Collisions
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Conservation of Momentum: Total momentum before = total
momentum after
Mu1 + mu2 = Mv1 + mv2
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Conservation of Energy: Total energy before = total energy
after
½Mu12 + ½mu22 = ½Mv12 + ½mv22
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Elastic collisions: zero energy loss
Impulse = Force x time
(Ns) = (N) x (secs)
Ideal Gases
Robert Brown investigated the movement of gas
particles – 1820s
• Air particles (O2 and N2) – too small
• Observe the motion of smoke grains
Microscope
Glass box
Smoke grain
(speck of reflected light)
Light
Ideal Gases
Pick 1 grain & follow its movement
- Jerky, erratic movement due to
collisions with (the smaller) air
molecules
Microscope
Glass box
Smoke grain
(speck of reflected light)
Light
Ideal Gases
STP = standard temperature and pressure
T = 273K, p = 1 atm
Average 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:
We can measure:
 Pressure (Nm-2)
 Temperature (K)
 Volume (m3)
 Mass (kg)
Moles
In the periodic table:
8
6
Oxygen = O 16
Carbon = C12
Helium = He 24
Mass number = bottom number = molar mass
• 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 Law
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Relates 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’ Law

Relates temperature & volume of the gas
If the gas is compressed:
volume decreases, temperature decreases
So keeping everything else constant:
V/T = constant or
VαT
V
-300
-200
0
100
-100
200
0
100
300
T (C)
400
T (K)
Pressure Law
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Relates temperature & pressure of the gas
If the gas is heated:
temperature increases, pressure increases
So keeping everything else constant:
p/T = constant or
pαT
p
0
T (K)
Ideal Gas Equation
The 3 gas laws can be written as a single equation
which relates the 4 properties mentioned earlier
pV = nRT
where R = universal gas constant = 8.31Jmol-1K-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
Summary
Vectors
 Projectiles
 Moments
 Power, Energy & Work
 Energy Changes
 Heat Capacity
 Newton’s 3 Laws
 Collisions
 Molecular Kinetic Theory
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