# P6-Further Mechanics and Thermal Physics

Circular Motion

• To cause an object to move with uniform circular motion a centripetal force is required.
• In uniform circular motion, the object has a constant speed (here the speed is scalar and the magnitude is constant, velocity as the vector is constantly changing along with its direction).
• The object is always accelerating as the direction of motion is constantly changing.
• The objects acceleration always acts towards the centre and this is called centripetal acceleration.
• To cause this acceleration, there must be a resulting force acting towards the centre (centripetal force)

F = I / T

v = velocity/ms-1

w = angular velocity/ rad s-1

f = frequency/ Hz (s-1)

a = acceleration / (ms-2)

F = centripetal force /N

m = mass / kg

T = time / s

w = v / r = 2πf

a=v2/r = w2r

F= mv2/r = mw2r

Motion in vertical circles-The centripetal force is the resultant force and remains constant.

Centripetal force is the resultant force of T (tension in the string) and mg.

Fc = T+ mg

Now the weight ‘fights against’ the tension and must be overcome, so T increases.

Fc = T – mg

Simple Harmonic Motion

It is a type of periodic motion or oscillation where the acceleration is directly proportional to the displacement, but acts in the opposite direction.

Phase difference ‘ᶲ’describes the relationship between two systems – normally expressed in radians.

ᶲ = 2π∆t/T

Mass on a spring                            x

Energy in SHM

Assuming that there is no friction or air resistance , so total energy remains constant.

Resonance

Natural Frequency= the frequency a system “likes’ to oscillate at.

System can be driven = Energy supplied to the system.

Resonance occurs when a system is driven at its natural frequency

At resonance, energy transfer will be greatest and the amplitude of oscillation will be maximum.

Damping

1. Reduces the amplitude of oscillation
2. reduces the “sharpness” of resonance peak and “flattens” it.

Thermal energy transfer

INTERNAL ENERGY- is the total of the random kinetic energy due to the motion of the molecule and the potential energy due to the molecules.

Potential Energy – is the energy as the result of the attraction of the molecules.

First law od thermodynamics:

The change in the internal energy is equal to the total energy transferred due to work done and heating.

Specific heat capicity (c) – is the energy required to raise one unit of mass of the object by one unit of temperature.

Latent Heat – total energy absorbed or released when a substance changes its physical state completely at a constant temperature.

Specific latent heat of fusion- is the quantity of heat required to change 1Kg of solid in to liquid at constant temperature.

Specific latent heat of vaporization – is the quantity of heat energy required to change 1Kg of liquid to vapors at constant temperature.

Ideal gases

Absolute zero: the lowest possible temperature, the temperature at which an object has minimum internal energy.

Ok = -273°C

Gas laws

Boyle law : states that

pressure is inversely proportional to volume at constant temperature.

Charles’ law: states that

volume is proportional to temperature at constant pressure.

Pressure law: states that

pressure is directly proportional to temperature at constant volume.

putting these laws together

A ideal gas is one that follows this relationship.

The ideal gas equation

Molecular mass = number of mass * molar mass

Avagodros constant Na: number of atoms in 1Kg of Carbon-12 is used to define the mole, its value is 6.022×1023mol-1.

Kinetic theory of gases

effect of temperature on the distribution of speed

Assumption of the kinetic theory of gases

1. The molecules are point molecules. the volume of each molecule can be compared to the volume of gas.
2. The molecules have no attraction or repulsion for each other, if they did, the effect would reduce the impact on the walls of container.
3. The molecules move around in continuous random motion
4. the collisions between the molecules are completely elastic.

Each collision with container surface is much shorter in duration than between the imparts.

Mean kinetic energy of molecules

Total kinetic energy