Year 11 DAS Physics Notes
Calculation Questions in Physics
Calculation questions in physics are like chicken nuggets: the numbers (meat) are coated by surrounding information.
The task is to strip away the coating to get to the numbers before calculating the answer.
Using Equation Triangles
Each triangle has at least 3 variables.
In a question, 2 variables will be given.
To find the equation for the unknown variable, cover the unknown in the triangle.
Write down the symbol for the unknown, followed by an = sign.
Write down the uncovered variables to the right of the = sign.
Example: speed, distance, time triangle.
Harvesting Marks in Calculation Questions: The 4-Step Process
Equation: Write down the equation you will use. (Equation triangle doesn't get a mark)
Substitution: Substitute the known values into the equation.
Numerical Answer: Write down the calculated value.
Unit: Write down the units of measurement for the calculated value.
Quantities and Measurement
Kilograms (kg) are used to measure mass (e.g. 1 kg).
Newton meter (spring balance) is used for measuring force in Newtons.
Scalar and Vector Quantities
Scalar: Quantities with only size (magnitude), e.g., mass, distance, speed, temperature.
Vector: Quantities with both size and direction, e.g., forces, displacement, velocity, acceleration.
Motion Definitions
Distance: Scalar; separation between 2 points.
Displacement: Vector; distance in a specified direction.
Speed: Scalar; distance travelled per unit time.
Velocity: Vector; displacement per unit time.
Acceleration: Vector; change in velocity per unit time.
Average Speed, Distance, and Time
Use the speed, distance, time triangle to derive the equations.
The calculated speed is the average speed.
Average\, speed = \frac{total\,distance\,travelled}{total\,time\,taken}
Average speed must be calculated by measuring distance and time, not directly measured.
Average Velocity, Displacement, and Time
Use the velocity, displacement, time triangle to derive the equations.
The calculated velocity is the average velocity.
Average\, velocity = \frac{total\,displacement}{total\,time\,taken}
Acceleration
Change in velocity per unit time.
Measured in m/s\text{}^2
\Delta v (delta v) represents the change in velocity.
v: final velocity
u: initial velocity
a: acceleration
t: time taken for the change in velocity
If u > v, then acceleration will be negative, indicating deceleration.
Calculating Average Velocity and Displacement During Acceleration
Avg\, vel = \frac{(v + u)}{2}
Example: A car accelerates from 20m/s to 100m/s in 5s. The average velocity is \frac{(100 + 20)}{2} = 60 m/s
Distance covered during acceleration: d = v \times t
So the car traveled 60 \times 5 = 300m during the acceleration.
Motion Graphs
Graphical representations of an object's motion.
Types:
Distance-time graphs (dtg's)
Displacement-time graphs (dtg's)
Speed-time graphs (stg's)
Velocity-time graphs (vtg's)
Gradient = slope; the gradient of a line = rise/run (vertical rise / horizontal run).
Distance-Time Graphs
Show how distance changes as time progresses.
Flat line = stopped.
Slope of constant upward gradient = constant speed.
Steeper slope = greater gradient = greater constant speed.
Speed = \frac{rise}{run} = \frac{distance\,travelled}{time\,taken}
Displacement-Time Graphs
Show how displacement from the origin changes as time progresses.
Flat line = stopped.
Slope of constant upward gradient = constant velocity away from the origin.
Steeper slope = greater gradient = greater constant velocity.
Downward slope = constant velocity towards the origin.
Velocity = \frac{rise}{run} = \frac{displacement\,travelled}{time\,taken}
Speed-Time Graphs
Show how speed changes with time.
Flat line = constant speed.
Slope of constant upward gradient = constant acceleration.
Steeper slope = greater acceleration.
Downward slope of constant gradient = constant deceleration.
Acceleration = \frac{rise}{run} = \frac{change\,in\,speed}{time\,taken}
Area under the speed-time graph = distance travelled.
Velocity-Time Graphs
Show how velocity changes with time.
Flat line = constant velocity.
Slope of constant upward gradient = constant acceleration.
Steeper slope = greater acceleration.
Downward slope of constant gradient = constant deceleration.
gradient = \frac{rise}{run} = \frac{change\,in\,velocity}{time\,taken} = acceleration
Area under the velocity-time graph = displacement.
Velocity-Time Graph for a Ball Thrown Up
As the object is thrown up, its velocity decreases due to gravity, eventually reaching 0.
As it falls, its velocity increases due to gravity but in the opposite direction (negative values).
The gradient gives the acceleration due to gravity.
The maximum height is calculated by the area of the triangle above the x-axis.
If the object returns to the start point, total displacement = 0.
Motion Graphs Summary (Gradients and Areas)
Gradient = steepness of the slope.
Upward slope = positive gradient.
Downward slope = negative gradient.
Flat horizontal line = gradient of 0.
Gradient = \frac{vertical\,rise}{horizontal\,run}
Gradients of distance-time graphs = speed.
Gradients of displacement-time graphs = velocity.
Gradients of speed-time graphs AND velocity-time graphs = acceleration.
Area under stg = distance
Area under vtg = displacement
Forces
Vector quantity (size and direction).
Measured in Newtons (N).
Examples: Lift, Drag, Thrust, Gravity.
Friction
Force opposing motion, acting in the opposite direction.
Occurs when surfaces move over each other.
Factors affecting friction: roughness of surface and weight of object.
Resultant Force
Measured in Newtons (N).
The resultant force (RF) is the overall force acting on an object.
The size of the RF determines the size of any acceleration.
Newton's 1st Law (Law of Balanced Forces)
If the forces acting on an object are balanced (equal in size but opposite in direction), there is no change in motion.
No change in motion = constant speed/velocity, i.e., acceleration = 0 m/s\text{}^2
If constant speed is mentioned, think balanced forces, and vice versa.
Newton's 2nd Law (Law of Unbalanced Forces)
If the forces acting on an object are unbalanced (unequal in size but opposite in direction), there is a change in motion.
Change in motion = change in speed/velocity, i.e., an acceleration.
Motion Flowchart
Speed constant? yes/no
Direction constant? yes/no
N1 (Newton's 1st Law)
N2 (Newton's 2nd Law)
Relationship Between Resultant Force, Mass, and Acceleration
The bigger the RF acting on an object, the greater the acceleration.
The greater the mass of an object, the smaller the acceleration with the same RF.
Investigating F=ma
As force increases, the size of the acceleration increases.
Draw a graph of Force (x-axis) and average acceleration (y-axis).
Mass, Weight, and Gravity
Mass: Measure of how much matter is in an object (independent of gravity), units = kg.
Weight: A downward acting force produced by a mass under the influence of gravity (dependent on gravity), units = N.
Gravity: Force pulling/accelerating objects to the center of a mass, units = m/s\text{}^2 or N/kg. On Earth, g = 10 m/s\text{}^2 or N/kg.
Relationship Between g, Mass, and Distance
As the mass of an object increases, so does the size of gravity it produces.
As the distance from a mass increases, the size of g decreases.
Vertical Motion Under Gravity – Free Fall
Initially, weight force and air resistance are unbalanced, so the object accelerates.
As speed increases, air resistance increases to balance weight, achieving constant (terminal) velocity.
Parachute opening causes air resistance to increase, resulting in unbalanced forces causing deceleration to a new safer terminal velocity.
Hooke's Law
When a load/force is applied to a spring, it will extend.
Extension = extended length – natural (unloaded) length.
Hooke's Law: Extension is proportional to load, provided the limit of proportionality is not exceeded.
If the load doubles, the extension doubles.
Hooke's Law Graphs
On a graph, extension is directly proportional to force up to the limit of proportionality.
If the spring exceeds this point, it has reached its elastic limit and will not return to its original length when unloaded.
Hooke's Law equation: F = k \times e
F = force (N), e = extension (cm), k = spring constant (N/cm)
k (spring constant) is unique to a spring and is the gradient of the graph.
Steeper line = greater gradient = greater k value = more force needed to extend the spring by 1cm.
Large k = “stiff” spring.
Graph Questions
Always check the axes’ labels!
If an axis is labelled length, the point where the line crosses this axis is the original (unloaded) length of the spring.
Hooke’s law is being obeyed where the line has a constant gradient.
The limit of proportionality is the point where the gradient changes (Hooke’s law no longer obeyed).
Pressure
Pressure is defined as force acting per unit area.
The standard unit of pressure is the N/m\text{}^2 or Pascal (Pa).
P = \frac{F}{A}
Pressure will be lowered when the area is increased and raised when the area is decreased
Moments – AKA Turning Effect
When a force is applied to an object that is free to rotate about a fixed point, a moment is produced.
Fixed point: pivot.
Moment: turning effect.
M = F \times d
F = force in N; d = perpendicular distance force acts from pivot (m or cm); M = moment (Nm or Ncm)
Moments can be clockwise or anticlockwise.
The moment increases if the applied force is moved further from the pivot.
Principle of Moments (Equilibrium)
When an object is in equilibrium (balanced), the sum of the anticlockwise moments = the sum of the clockwise moments (The Principle of Moments).
At equilibrium: sum\,acwm = sum\,cwm
F1 \times d1 = F2 \times d2
In Qs equilibrium is often implied using the terms – just lift, just move, and balance etc
Centre of Gravity/Centre of Mass
The center of mass/gravity of an object is the point through which the weight of an object appears to act.
If an object is supported at its CoG, it will balance as sum\,acwm = sum\,cwm
In regular objects, the CoG is at the center; for irregular objects, it moves towards the region of most mass.
Centre of Gravity: Equilibrium and Stability
Stability: A measure of how difficult it is to topple an object.
Increased stability is achieved by lowering the CoG and increasing the base area.
An object will topple when the CoG acts outside the base area.
Stable equilibrium: low CoG, wide base.
Unstable equilibrium: high CoG, narrow base.
Neutral equilibrium: CoG always over base (spheres and cylinders on their side).
Density
Density is defined as mass per unit volume.
Mass can be in g or kg; volume in cm\text{}^3 or m\text{}^3; density in g/cm\text{}^3 or kg/m\text{}^3
D = \frac{m}{V}
m = mass
V = Volume
Any object with an overall D less than the D of the surroundings will float.
Density of Regular Solids
Measure the length, width, and height using a ruler.
Calculate the volume using V = length \times cross-sectional\,area
Zero a mass balance, place the object on the balance and read off the mass.
Determine the density using Density = \frac{Mass}{Volume}
Density of Irregular Objects (1)
Fill a measuring cylinder to a known level, add the object (having weighed it).
The object will displace its own volume of water, measure and record the new level.
\text{Volume of object = new value – previous value}
D = \frac{m}{V}
Density of Irregular Objects (2)
Alternatively, a Eureka can may be used – fill the can to the level of the outlet spout and gently place the object into it. Water will be displaced out of the can and collected in a measuring cylinder.
D = \frac{m}{V}
Density of a Liquid
Place a measuring cylinder on a mass balance and note the mass of the empty cylinder.
Fill the measuring cylinder with the liquid to any value and read off the volume.
Read off the mass of the measuring cylinder and liquid.
The mass of the liquid can be found by subtracting the mass of the empty measuring cylinder from the mass of the filled measuring cylinder.
Determine the density using Density = \frac{Mass}{Volume}
Kinetic Theory (Differences in Density)
All matter is made up of particles that have mass.
The further apart the particles are, the less mass there will be in any given volume, decreasing density.
Densities: D\text{sol} > D\text{liq} > D\text{gas}
Types of Energy
Electrical energy (EE), Kinetic energy (KE), Sound energy (SE), Radiant energy (RE) (including light energy (LE), radio waves, microwaves, and X-rays), Heat energy (HE).
Three types of stored/potential/“hidden” energy: chemical energy (CE), nuclear energy (NE), and potential energy (PE) (gravitational PE (gPE) and elastic PE (ePE)).
Energy is measured in Joules (J).
Conservation of Energy Principle
Energy cannot be created or destroyed but can be converted from one form to another.
Energy Transfers and Transfer Diagrams
Energy transfer diagrams show the input and output energy in an energy transfer.
Heat Energy (HE) is always produced.
Efficiency
Efficiency is a measure of the proportion of the INPUT energy that becomes useful/desired OUTPUT energy.
Expressed as a % (e.g., 50%) or a decimal (e.g., 0.5).
It will never be 100% or 1.0, as no energy transfer is 100% efficient (there is always waste energy).
Cannot be more than 100% or 1, as this would mean energy had been created.
Calculating Efficiency
Eff = \frac{uo}{ti}; uo = ti \times eff; ti = \frac{uo}{eff}
Eff = efficiency, uo = useful output , ti = total input
Energy Resources
The main uses of energy resources are transport and generating electricity.
Fossil fuels (C, O, G) account for a high percentage of energy resources.
About 84% of the world's energy usage in 2019 came from fossil fuels.
Renewable and Non-Renewable Resources
Non-renewables (not replaced within 50 years): c, o, g, and nuclear.
Renewables (not used up or will be replaced within 50 years): solar, wind, wave, tidal, hydro, geothermal, and biomass (e.g., wood).
All but nuclear and geothermal are derived directly or indirectly from energy from the sun.
Combustion of fossil fuels contributes to global warming as CO\text{}_2 is produced.
Advantages and Disadvantages of Renewable and Non-Renewable Resources
Renewables
Advantages: won't run out, non-polluting.
Disadvantages: unreliable supply, large areas needed for high outputs.
Non-Renewables
Advantages: reliable, high outputs.
Disadvantages: will run out, polluting.
Generating Electricity (EMI)
AC generator.
Electricity is generated using Electro-Magnetic Induction (EMI).
When a wire is subjected to a changing magnetic field, a current is made/induced.
Done either by moving a magnet inside a coil of wire (dynamo) or moving a coil of wire inside a magnet (generator).
Generating Electricity
Power stations convert the stored CE or NE in the fuel to EE involving a number of steps, including producing steam which spins a turbine, which rotates the coil in the generator.
Renewables turn the generator directly.
Gravitational Potential Energy (gPE) / Ep
Objects above ground level have stored gPE.
gPE= m \times g\times h
m = mass (kg); g = gravity (10 m/s\text{}^2 on Earth); h = height (m)
m = \frac{gPE}{g \times h}
g = \frac{gPE}{m \times h}
h = \frac{gPE}{m \times g}
Kinetic Energy (KE) or Ek
Movement energy.
The amount of KE an object has depends on its mass and velocity.
KE = \frac{1}{2} \times m \times v^2
m = mass; v = velocity.
KE to gPE (and Back Again)
When a ball is thrown up, its KE is converted to gPE. As it falls, gPE becomes KE.
At its maximum height, all its KE is now gPE. At the bottom, all its gPE is now KE (assuming no energy losses).
Total energy (TE) = gPE + KE.
We can calculate the maximum height from the original KE and maximum KE from the original gPE.
Work
Work is done when a force is moved through a distance or when energy is converted from one form to another.
Unit: Joule (J).
W = F\times d
W = work (J); F = force (N); d = distance (m)
The force in Qs is often a weight force, and the minimum force required to lift a weight IS the weight.
A mass in kg must be converted to a weight force (in N) by multiplying it by 10.
The distance used to calculate work done must be in the same direction as the force!
Work Done and PE Gained / KE Lost
Work done in raising an object = the gPE gained by the object.
Similarly, gPE stored by a raised object = the maximum work that can be done as the object falls.
When a moving object is brought to a halt, work is done by the frictional forces (e.g., the brakes).
The amount of work done is the same as the KE of the object.
KE lost = work done by brakes.
Simple Machines – The Ramp
Simple machines (e.g., ramp, lever, pulleys) make work easier by reducing the effort force (however, this reduced effort must be put through a greater distance).
Power
Power is the rate at which work is done (work done per second).
Unit: Watts (W).
1 W = 1 J/s.
P=\frac{W}{t}
P = power, W = work, t = time
Atomic Structure
Central nucleus containing protons and neutrons surrounded by electrons in orbits/shells.
Protons and neutrons are nucleons.
Mass of proton and neutron = 1.
Mass of electron is negligible (1/1840).
Proton: +1 charge, electron: -1 charge, neutron: no charge (0).
Atomic Number, Atomic Mass, and the Nucleus
Atomic mass = p + n (sum of protons and neutrons in the nucleus).
Atomic number (proton number) = p AND e (number of protons in the nucleus and electrons orbiting the nucleus).
n = atomic\,mass – atomic\,no. (n = A – Z)
The atomic number (number of protons) determines the element.
Isotopes
Atoms with the same number of protons (at. no.) but different numbers of neutrons.
Isotopes have different atomic masses.
Background Radiation and Its Sources
Radiation that constantly surrounds us.
Sources: radon gas, C-14 in food, rocks, and cosmic rays.
The Becquerel (Bq) and Measuring Radiation
Radiation is measured using a Geiger counter. Unit: Becquerels (Bq).
1 Bq = 1 disintegration per second
When measuring radioactivity, make a background count first & then subtract to produce a corrected count rate.
Nuclear Decay
Radioisotopes are isotopes with an unstable combination of protons and neutrons.
Unstable nuclei undergo random, spontaneous decay, releasing ionizing radiation (alpha, beta, and gamma (one or more of which can be released during a decay event)).
The resulting nucleus is called a daughter nucleus/isotope.
Ionizing Radiation (Alpha, Beta, and Gamma)
When alpha, beta, and gamma radiations collide with molecules, they eject electrons (ionization).
Ionization can cause mutations and cancer.
Ionization damage strength: Alpha > Beta > Gamma.
Minimizing Risk from Ionizing Radiation
Minimize duration of exposure (wear radiation dosimeter badges).
Maximize distance – no direct contact.
Stay behind shielding and wear protective (preferably lead-lined) clothing.
Types of Radiation Emitted by Radioactive Isotopes/Elements
Alpha, Beta, and Gamma
Penetration Power
Gamma > Beta > Alpha
Alpha stopped by Paper. Beta stopped by Aluminium. Gamma stopped by Lead
Alpha Particles
Consist of 2 protons + 2 neutrons (Helium nucleus).
Relatively large, heavy, and slow.
Daughter nucleus mass decreased by 4, atomic number decreased by 2 - a new element is produced.
Beta Particles
High-energy electron emitted from a nucleus when a neutron turns into a proton.
Faster and lighter than alpha particles.
Daughter nucleus remains the same atomic mass, but the atomic number increases by 1 (a new element is produced).
Gamma Rays
Type of electromagnetic radiation (like light).
Travels as a wave at the speed of light.
No change in mass or atomic number during gamma decay.
Nuclear Decay Equations
Show the parent nucleus, the decay particle, and daughter nucleus of alpha, beta, or gamma decay.
The top numbers above each symbol are the mass numbers - the left and right will add up to the same value.
The bottom numbers are the proton/atomic numbers - the left and right will add up to the same value.
Decay and Half-Life
An element’s half-life is the time taken for 50% (or ½) of the radioactive nuclei to decay, or the count rate to fall by 50% (or ½).
Half-Life and Radiocarbon Dating
When organisms die, the amount of radioactive carbon-14 decreases.
The amount of radioactive Carbon-14 present in a sample allows us to estimate the sample's age.
Uses of Radiation
Dependent on their penetrating power, ability to damage cells through ionization, and half-lives of the radioisotopes producing them.
Uses in Medicine: (i) Radiotherapy
Gamma has the greatest penetrating power, so it can be used to kill cancer cells.
(ii) Sterilizing Equipment
Delicate medical equipment can be sterilized using gamma radiation.
Uses in Agriculture/Food Industry: (i) Sterilizing Fresh Food
Food can be sterilized using gamma radiation, prolonging its shelf-life.
(ii) Monitoring Fertilizer Uptake
Using radioisotopes in fertilizers, we can track and trace the deposition of nutrients within a plant.
Uses in Industry: (i) Maintaining Uniform Thickness
Beta radiation ensures metal sheets are the correct thickness.
(ii) Tracer Studies – Detecting Leaks
Gamma has greatest penetrating power, so can be used to detect leaks from pipes.
Uses in the Home: The Smoke Detector
Contain the alpha-emitting element Americium.
Smoke reduces the number of alpha particles reaching a detector, which triggers the alarm.
Nuclear Power: Fission and Fusion
Fission
Energy released when a large nucleus splits into smaller daughter nuclei.
A Uranium-235 nucleus, hit by a neutron and disintegrates releasing energy and 2 more neutrons - chain reaction.
Nuclear Power Plant
Heat released during fission produces steam which turns a turbine which drives a generator.
Advantages: reliable, high supply which doesn’t produce CO\text{}_2
Disadvantages: very expensive, dealing with nuclear waste and other contaminated equipment is costly and dangerous.
Fusion
2 smaller nuclei fused together to form a larger nucleus and release energy (x4 per kg than fission; x4million per kg coal!).
The most common fusion reaction involves isotopes of H, deuterium (H-2) and tritium (H-3).
It requires huge temperatures to overcome the repulsion between the 2 positively charged nuclei.
Controlled and Uncontrolled Fusion
Uncontrolled fusion – a H-bomb.
Controlled – if we could control it, it would be a source of unlimited power.
The main difficulty is in containing the H plasma at a high enough temp for long enough for a reaction to take place.
At present, we get less energy out than we put in!
Ignition Achieved! Nuclear Fusion Power Now Within Reach
In December 2022, for the first time, more energy was obtained than was put in using an experimental fusion reactor.