HL Physics Revision Notes

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Sachin

Physics Revision

Topic 1: Physics and Physical Measurement:

The realm of physics:

The order of magnitude is i.e. 10x.

Range of masses (kg): 10-32 (electron) to 1052 (mass of the observable universe)

Range of lengths (m): 10-15 (diameter of proton) to 1026 (radius of universe)

Range of times (s): 10-23 (passage of light across a nucleus to 1019 (age of the universe)

Measurement and uncertainties:

Fundamental units:

Derived units are different combination of the fundamental units

For example speed = distance/time = meters/seconds =m/s =ms-1

Remember to state answers in the format ms-1

Important Prefixes:

Random errors are errors in measurement caused by different factors

Random errors include the readability of the instrument and the effects of a change in surroundings. Repeated readings do reduce random errors.

Systematic errors are errors due to faulty equipment/calibration.

Systematic errors include an instrument being wrongly calibrated. Repeated readings do not reduce systematic errors.

Individual measurements: the error is ± the smallest value e.g. .5mm

When we take repeated measurements and find an average, we can find the uncertainty by finding the difference between the average and the measurement that is furthest from the average.

A precise experiment is one with a small random error, i.e. the more significant figures the more precise.

An accurate experiment is one with a small systematic error, i.e. the nearer the real value the more accurate.

Give answers to the same amount of significant figures as the least precise value used.

If you have the measurement for a football pitch of 100m±1m

The absolute uncertainty is 1m

The fractional uncertainty is 1/100 = .01

The percentage uncertainty is .01 x 100 = 1%

For addition and subtraction, the absolute uncertainties can be added

When 2 quantities are multiplied or divided the overall uncertainty is equal to the addition of the percentage uncertainties

Powers = # of power x uncertainty.

For other functions such as trigonometric function, the mean, highest and lowest answers may be calculated to obtain the uncertainty range.

Uncertainties in graphs: Error bars. Note that a line of best fit should pass through all error bars. Some easy ways to get round this are just to plot the first and last value of error bars or just the worst value and assume the same for all.

Uncertainty in slopes is shown by max and min gradients using the first and last gradients

The same can be done for the uncertainty in intercepts.

1.3 Vectors and Scalars:

A vector has magnitude and direction. A scalar only has magnitude. E.g. all forces are vectors.

Vectors: Displacement, Velocity, Acceleration, Force, Momentum

Scalars: Distance, Speed, Mass, Temperature

Additional:

Proportional is a straight-line that passes through the origin.

Gradients units are the y-axis/x-axis i.e. rise/run. Only if the x-axis is a measurement of time des the gradient represent the rate at which the quantity on the y-axis increases.

Area under a straight-line graph is y-axis x x-axis.

Topic 2: Mechanics:

2.1 Kinematics:

Displacement is a vector quantity and is the distance moved in a particular direction

Velocity is a vector quantity and is the rate of change of displacement

Speed is a scalar quantity and is the rate of change of distance

Acceleration is a vector quantity and is the rate of change of velocity

Average velocity is the change in displacement divided by the change in time.

Instantaneous velocity is the change in displacement as the change in time becomes infinitely small.

Speed and acceleration work in the same way

Equations for uniformly accelerated motion can only be used when the acceleration is constant, i.e. uniformly accelerating in the same distance.

Equations of uniform motion:

u = initial velocity

v = final velocity

a = acceleration

t = time

s = distance

v=ut+at

s=(u+v/2)t

v2=u2+2as

s=ut+.5at2

In absence of air resistance, all falling objects have the same acceleration of free-fall, independent of their mass, 9.8 ms-2

When the drag force reaches the magnitude of the force providing the acceleration, the falling object will stop accelerating and fall at a constant velocity. This is called the terminal velocity

Relative velocity is determined by frames of reference i.e. if one car is at 20 and another is at 25, then from the first car the other car looks to be going at 5.

Additional: Ways to record the motion of velocity/acceleration: light gate, strobe photography, ticker timer.

2.2 Forces and Dynamics:

Weight = mg

Forces include: gravitational force, friction, tension, the normal force, etc

In a free-body diagram only one object is chosen and all the forces and shown and labelled.

Newton’s first law of motion states that an object continues in uniform motion in a straight line or at rest unless acted upon by a resultant external force. The law of inertia.

An example of this is a ball rolling on a frictionless surface will roll forever unless an external force acts on it.

The condition for translational equilibrium is that the net force on an object is zero.

Objects in equilibrium must either be constantly at rest or moving with constant velocity. Static equilibrium would be a book on a table. Dynamic equilibrium would be a book being dragged across a table at a constant speed.

F=ma. The net force acting on an object is the product of the objects' mass and the net acceleration of the object.

Linear momentum is the product of mass and velocity. P=mv. It is measured in kg ms-1.

Impulse in the change in momentum (I=Ft). Impulse also equals (p’ –p) Ft=mv

The impulse of a time-varying force is represented by the net area under the function (the integral) of the force-time graph.

Law of conservation of momentum: The total momentum of a system remains constant provided there is no resultant external force.

Newton’s third law states that when a force acts on a body, an equal and opposite force acts on another body somewhere in the universe.

One example would be two roller-skater’s pushing off one-another

Additional:

Mass is the amount of matter contained in an object measured in kg, whilst weight is a force measured in N.

2.3 Work, energy and power:

Work done = Fs cosΘ.

The amount of energy transferred is equal to the amount of work done

If the force and displacement are in the same direction then Work done = Fs

Work is measured in N m = Joules.

The area below a Force-displacement graph is equal to the work done.

Work done in compressing or extending a spring = .5 kx2

Gravitational potential energy = mgh

Kinetic energy is the energy a body possesses due to motion. =.5mv2

Principle of conservation of energy: Energy cannot be created or destroyed, it just changes form.

0.5mv2=mgh

There are many different forms of energy.

Thermal energy includes the kinetic energy of atoms and molecules.

Chemical energy is the energy that is associated with the electronic structure of atoms and is therefore associated with the electromagnetic force. An example where chemical energy is converted into kinetic (thermal) energy is the combustion of carbon. Carbon combines with oxygen to release thermal energy along with light and sound energy.

Nuclear energy is the energy that is associated with the nuclear structure of atoms and is therefore associated with the strong force. An example is the splitting of uranium nuclei by neutrons to produce energy.

Electrical energy is associated with electric current. Boiling water can turn a turbine with a magnet which rotates in a coil to induce electrical energy.

An elastic collision is when there is no mechanical energy that is lost. In other words, the total kinetic energy of the objects is the same before and after the collision. An inelastic collision is where mechanical energy is lost. Almost always in reality collisions are inelastic as energy is lost as sound and friction.

Power is the rate at which energy is transferred or which work is done.

Power = work done/time or energy transferred/time.

Power = force x velocity

Efficiency is the ratio of useful energy to the total energy transferred.

Efficiency = useful/total

Uniform Circular Motion: An object going round a circle at constant speed

For an object to move around in a circle, it must be travelling in a direction at the tangent to the circle where the object is at, and direction of the force being applied must be perpendicular to the direction the object is travelling in. The direction of the force is pointing to the centre of the circle

The acceleration of a particle travelling in a circular motion is centripetal acceleration

The force needed to cause the centripetal acceleration is called the centripetal force.

Centripetal force does not do any work as work done = force x distance in the direction of the force.

Examples of forces which provide centripetal forces are gravitational forces (planets orbiting in a circle), frictional forces (car driving in circles), magnetic forces or tension (string). F=ma. a = v^2/r. Therefore, F=mv^2/r

Topic 3 Thermal Physics:

Temperature is a scalar quantity that gives indication of the degree of hotness or coldness of a body.

Temperature determines the direction of thermal energy transfer between two bodies in contact; from the body at higher temperature to the body at lower temperature.

Thermal equilibrium occurs when all parts of the system are at the same temperature. There is no exchange of heat.

T(Kelvin) = T(Celsius) +273. They have different zero points.

Internal energy of a substance is the total kinetic and potential energy that molecules possess. They have kinetic energy from their random/translational/rotational movement and potential energy from the intermolecular forces.

Temperature is a measure of the average kinetic energy of the molecules in a substance.

A mole is the basic SI unit for amount of substance. One mole of any substance equals the same number of atoms as 12 grams of carbon.

Molar mass is the mass of one mole of substance. If an element has mass number A, then the molar mass will be A grams.

Avogadro’s constant is the number of atoms in 12 g of carbon-12. It is 6.02 x1023.

3.2 Thermal properties of matter: 

Thermal capacity (C) is the energy required to raise an object’s temperature by 1K. C=Q/ΔT

Specific heat capacity is the energy required to raise a unit mass of substance by 1K. c=Q/(mΔT)

The difference is that thermal capacity measures the substance’s ability to absorb heat as an entire object, whereas specific heat capacity measures the substance’s ability to absorb heat per unit mass. 

If an object is raised above room temperature it starts to lose energy. The hotter it becomes the greater rate at which it loses energy.

Molecules are arranged in different ways depending on the phase of the substance, (i.e. solid, liquid or gas)

Solids: Fixed volume and fixed shape. The molecules vibrate about a fixed position. The higher the temperature the greater the vibrations.

Liquids: Fixed volume but shape can change. Molecules are vibrating but not completely fixed in position, still strong forces between molecules.

Gases: Not fixed volume or shape, will expand to fill the container. Forces between molecules are weak. Molecules are essentially independent but will occasionally collide.

While melting, vibrational kinetic energy increases and particles gain enough thermal energy to break from fixed positions. Potential energy of system increases

•         While freezing, particles lose potential energy until thermal energy of the system is unable to support distance between particles and is overcome by the attraction force between them. Kinetic energy changes form from vibrational, rotational and part translational to merely vibrational. Potential energy decreases.

•         While evaporating, certain particles in the liquid gain enough potential energy to escape the intermolecular bonds as a gas. The escape of the higher-energy particles will lower the average kinetic energy and thus lower the temperature.

•         While boiling, substance gains enough potential energy to break free from inter-particle forces. Similar to evaporation, the only difference being that energy is supplied from external source so there is no decrease in temperature

When condensing it’s the opposite of boiling.

During a phase change, the thermal energy gained or lost will go towards increasing or decreasing the potential energy of the particles to either overcome or succumb to the inter-molecular force that pulls particles together. In the process, the average kinetic energy will not change.

The energy given to molecules does not increase kinetic energy so it must increase potential energy. Intermolecular bonds are broken are being broken and this takes energy. When a substance freezes, bonds are created and this releases energy. Molecules do not speed up during a phase change.

Evaporation differs from boiling as evaporation is a change from the liquid state to the gaseous state that occurs at a temperature below the boiling point.

Specific latent heat is the amount of energy per unit mass absorbed or released during a change of phase. Specific latent heat (L). L=Q/m

Fusion: The change of phase from solid to liquid

Vaporization: The change of phase from liquid to gas

Pressure is the force gas molecules exert due to their collisions (with an object). P=F/A i.e. force per unit area.

Assumptions of the kinetic model of an ideal gas:

Newton’s laws apply to molecular behaviour

There are no intermolecular forces

The molecules are treated as points

The molecules are in random motion

The collisions between molecules are elastic

There is no time spent in these collisions.

Decrease in volume results in a smaller space for gas particles to move, and thus a greater frequency of collisions. This results in an increase in pressure.

PV/T = PV/T

Topic 4 Oscillations and Waves:

Examples of oscillations include the swinging of a pendulum

Displacement (x) is the instantaneous distance of the moving object from its mean position

Amplitude (A) is the maximum displacement from the mean position

Frequency (f) is the number of oscillations completed per unit time. Measured in Hertz (Hz)

Period (T) is the time taken for one complete oscillation. T=1/f

Phase difference is a measure of how “instep” different particles are. If they are 180 degrees or (pi) off, they are completely out of phase by half a cycle.

Simple Harmonic Motion (SHM) is motion that takes place when the acceleration of an object is always directed towards and is proportional to its displacement from a fixed point.

This acceleration is caused by a restoring force that must always be pointed towards the mean position and also proportional to the displacement from the mean position.

a=-w2x where w is the angular frequency and is a constant. The negative sign signifies that acceleration is always pointing back towards the mean position.

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4.1.5 p 34 4.1.6

4.2 Energy changes during simple harmonic motion (SHM):

During SHM energy is interchanged between KE and PE

If there are no resistive forces then energy remains constant and the oscillation is said to be undamped.

Ek=.5mv2=.5mw2(A2-x2)

Ep=.5mw2x2

Total energy, Et=Ek+Ep=1/2mw2A2

4.3 Forced Oscillations and Resonance:

Damping involves a frictional/dissipative force that is always in the opposite direction to the direction of motion of the oscillating particle.

As the particle oscillates it does work against this force and loses energy

Underdamping: The resistive force is so small that a small fraction of energy is removed every cycle. Time ...

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