1. Mechanics & Molecular Kinetic Theory

2. Contents
Mechanics
Molecular Kinetic Theory

3. Mechanics 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)

4. Mechanics
Distance vs. Time graph:

5. Mechanics
Speed vs. Time graph:

6. Mechanics Forces and Vectors: Examples:
- scalar = speed (1 quantity… no direction)
- vector = velocity (2 quantities… speed & direction)
Other vector quantities:
- displacement
- momentum
- force
Vectors can be added to produce a resultant quantity

7. Mechanics
Adding vectors:
And again… + = - =

8. Mechanics Angular mechanics: Fx = F cos  Fy = F sin 
Weight always faces downwards
Force on road is perpendicular to motion

9. 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

10. Mechanics 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)
- 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

11. 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 (d/t = speed)
power = force x speed
P = Fv

12. 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
Potential Energy:
potential energy = weight × distance moved against gravity
(Nm) = (N) x (m)
Kinetic Energy:
kinetic energy = ½ mass x velocity2
(J) = (kg) x (m/s2)

13. Heat Capacity
Heat capacity (c): quantity of heat required to raise the temperature of a unit mass by 1°K
Heat flow = m × c × delta T
(J) = (kg) × (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

14. 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
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
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

15. Collisions
Conservation of Momentum: Total momentum before = total momentum after
Mu1 + mu2 = Mv1 + mv2
Conservation of Energy: Total energy before = total energy after
½Mu12 + ½mu22 = ½Mv12 + ½mv22
Elastic collisions: zero energy loss
Impulse = Force x time
(Ns) = (N) x (secs)

16. 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

17. 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

18. 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

19. If we have a box filled with gas:
We can measure:
Pressure (Nm-2)
Temperature (K)
Volume (m3)
Mass (kg)

20. Moles In the periodic table: Oxygen = O Carbon = C Helium = He8 6 2 16 16 12 12 4 4
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

21. Boyle’s Law 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
1/V V

22. 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 V α T V
T (C)
T (K)

23. Pressure Law Relates 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)

24. which relates the 4 properties mentioned earlier
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

25. Summary Vectors Projectiles Moments Power, Energy & Work
Energy Changes
Heat Capacity
Newton’s 3 Laws
Collisions
Molecular Kinetic Theory