Physical Sciences Paper 1: Last Push Revision

Newton's laws

• Memorise the following terms and aspects

• Practice and master how to draw a free-body or force diagram
  Listing possible forces you might come across:
  • Gravitational force or weight (F_g or w), for any object having a mass
  • Normal force (N), for all objects resting or moving on a surface
  • Frictional force (Static friction f_s or Kinetic friction f_k)
  • Air friction (f_air), the question will state when to consider air friction
  • Tension (T), an object pulling another with a string/rope
  • Action-reaction forces, an object pushing another by physical contact, no string F_{A on B} and F_{B on A}
  • Applied force
• Remember the Action-reaction force
  • The reaction force to the weight of an object is the Force that the object exerts on the Earth
  • Always think of Newton's third law. The reaction force to the Force that object A exerts on object B is the Force that object B exerts on object A
• After drawing a free-body diagram you must Draw a simplified free-body diagram that show ONLY forces that act parallel to the motion or displacement of the object
  E.g. Draw a free-body diagram of all forces acting on the block shown below considering that the block moves at constant velocity to the right

• Master how to write the expression of the net force (F_net) acting on each object
  Like in the example above; F_net = F_x - f_k
• Always take the direction of motion of the object as positive
• The net force is zero (F_net = 0) if the object is stationary or moves at constant velocity
• Calculating different forces and the F_net expression

Gravitational force (weight), F_g or w

The gravitational force is calculated as F_g = m.g

• If the object lies on a Horizontal surface, DO NOT include F_g in the F_net expression.
• If the object lies on an inclined surface, ALWAYS include F_g// (F_g// = m.g.sinθ) in the F_net expression.
• If the object moves vertically, up or down, you should include F_g in the F_net expression

Normal force (N)

• NEVER include the normal force in the expression of F_net
• Calculating the normal depends on the surface (horizontal or inclined) and the applied force (parallel to the surface or making an angle with the surface)
• Memorise and master how to calculate the Normal force for these scenarios

Friction (f)

• Always include friction, if it is present, in the F_net expression
• Frictional force always acts opposite to the motion of the object
• If you take the direction of motion as positive, then friction will have a negative sign when substituting it in the F_net expression.
• To calculate the magnitude of frictional force:

• If coefficient of friction is given
  • Use the formula f_smax = μ_s.N for static friction and
  • Use the formula f_k = μ_k.N for kinetic friction
• If coefficient of friction is not given
  • Make use of the F_net expression to find friction.

Tension (T)

• Tension is a force developed in (or transmitted through) a rope or string
• There is no specific formula to calculate the tension as it is considered as an applied force.
• You will generally find tension T in the F_net expression
• The direction of tension goes to the side of the object where the string is attached. So if the string is attached to the left side of the object, the tension pulls it to the left. If the string is attached at the top of the object, the tension goes upwards
  e.g.

Note that the string is attached to the right side of X so, the Tension pulls block X to the right. Equally so, the tension pulls block Y to the left.

• If there are two are in contact and one pushes another, then we have an action-reaction pair of forces

Block X experiences a force due to Y (F_YonX) pushing it to the left
Block Y experiences a force due to X (F_XonY) pushing it to the right
These two forces are equal and act in opposite direction. But they do not cancel each other because they act on different objects.
In calculations, treat them the same way you treated Tension

Applied force (F)

• The applied force must always be included in the F_net expression
• If the applied force acts at an angle α relative to the surface, then only the component of the force parallel to the surface (Horizontal component), F_x, must be included in the F_net expression.
  This component is calculated as F_x = F cos α

Calculations involving Newton's laws

• Draw a free body diagram of ALL forces for each object (Sure case marks)
• Draw a free body diagram showing ONLY forces acting parallel to the motion/surface
• Take the direction of motion as positive
• Write the F_net expression for each object using vector sum of forces (F_net = ΣF)
• Write the formula F_net = m.a (a sure case 1 mark)
• Equate the two expressions for F_net
  Σ F = m.a
• If there is only ONE unknown in the equation, solve for it.
• If there are two unknowns, a and T, in both equations then solve the simultaneous equations.

Newton's law of universal gravitation

• Memorise the law
• Use the formula F = G.m₁.m₂/r²
• Other formulae to use under this topic are g = G.M/r² and F_g = m.g

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Newton's laws exam questions Quiz on this topic

Vertical projectile motion

• Memorise and master the following terms and aspect:

Equations of motion

1. v_f = v_i + aΔt
2. v_f² = v_i² + 2aΔy
3. Δy = v_iΔt + ½aΔt²
4. Δy = ((v_i + v_f)/2) Δt

• Remember to use the formula Δx = v·Δt if the motion of an object moving at a constant velocity is involved. The object can be a Hot-air balloon, a Helicopter, a rocket…
• Note that there are only five variables (terms) to deal with for this topic:
  • Initial velocity: v_i (vector quantity)
  • Final velocity: v_f (vector quantity)
  • Displacement: Δx (vector quantity)
  • Acceleration: a (vector quantity)
  • Time interval: Δt (scalar quantity)
• Notice that each equation has got FOUR terms, and the value of acceleration a, that is 9,8 m·s^-2, is known (Constant). So practically three terms to focus on. The question statement will provide information about 2 terms and ask you to find the third one (the unknown).
• Always consider two points (positions) before attempting any calculation: A starting point and an end point for the object's motion. This must be informed by the question you are about to answer.
  The velocity at the starting point is the initial velocity and the velocity at the end point is the final velocity.
  The displacement Δx is the length between the starting point and the end point. Ignore the path taken by the object to move from start to end.
  So between the two positions, play with the variables v_i, v_f, Δx and Δt to select a suitable formula and solve the problem.
• The choice of direction is very CRITICAL for Vertical projectile motion. The choice of direction imposes the SIGN of acceleration a (+9,8 or −9,8).
  So if you take UPWARDS as positive, the sign of acceleration will be NEGATIVE (−9,8) in ALL your calculations, REGARDLESS of whether the object is moving upwards or downwards. Equally so, if downwards is taken as positive, acceleration will be positive in all calculations.
• Master these signs allocation after choosing the direction: Stick to only ONE

• Remember that the mass of the object is not necessary for equations of motion. Note that if the mass of the object is given the possibility is that there would be integration of momentum (p = m·v), change in momentum (Δp = m(v_f − v_i)) or impulse/Newton's second law in terms of momentum (F_net·Δt = Δp) involved.
• If two objects are given, the first thing is to identify which quantities (v_i, v_f, Δx or Δt) are the same for both objects.
• Get familiar and master all possible scenarios about Vertical projectile motion.

Drawing or interpreting graphs of motion of a projectile

Position - time graph

• Remember that the position - time graph of a projectile is a curve.
  The x-axis corresponds to the position of the observer; it is referred to as the ZERO-POSITION.
  E.g. an object is thrown vertically upwards from the top of a building and hits the ground below the throwing point after some time.

Velocity - time graph

• Remember that the velocity - time graph of a projectile is a straight line with a positive or negative gradient.
• Note that the x-axis, where the velocity is zero, is the lowest value with regards to the velocity. Each segment of the line drawn towards the x-axis implies a decrease in velocity, regardless of whether the line is above or below the x-axis. Any segment of line drawn away from the x-axis implies an increase in velocity.
  E.g. Two graphs that represent the same scenario

• Segment A - B, the line is drawn directed TOWARDS the x - axis. So from A to B, the velocity DECREASES.
  Segment B - C, the line is drawn directed AWAY FROM the x - axis. So from B to C, the velocity INCREASES.
• The gradient of velocity - time graph represents the acceleration.
• The area between the line and the x - axis represents the displacement.

Acceleration - time graph

• Remember that the acceleration of a projectile is constant.
• The acceleration - time graph is a straight horizontal line.
• The horizontal line is drawn above the x-axis from +9,8 if Downwards was taken as positive.
• The horizontal line is drawn below the x-axis from −9,8 if Upwards was taken as positive.

Marks allocation

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Vertical projectile motion exam questions Quiz on this topic

From the pack: Newton's laws tip page

Tip sheet written for this guide.

Key terms: learn these word for word

Formulas

• Momentum: p = mv (vector, unit kg·m·s^-1)
• Change in momentum: Δp = mv_f − mv_i = m(v_f − v_i)
• Impulse: F_netΔt = Δp = mv_f − mv_i (unit N·s, which equals kg·m·s^-1)
• Conservation of momentum: Σp_i = Σp_f, e.g. m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f
• Objects that stick together: m₁v_1i + m₂v_2i = (m₁ + m₂)v_f
• Explosion from rest: 0 = m₁v_1f + m₂v_2f
• Elastic check: ΣE_k,before = ½m₁v_1i² + ½m₂v_2i² compared with ΣE_k,after

Marks-earning tips

• Write down your positive direction first (e.g. "Take to the right as positive"). Velocities in the opposite direction are then negative.
• Momentum and impulse are vectors: give magnitude AND direction when the question asks for momentum, velocity or impulse.
• Every definition of the conservation principle must say "in an isolated (closed) system", or you lose that mark. The system mark is only given if it is used together with momentum.
• Start every calculation with the formula: Σp_i = Σp_f or F_netΔt = Δp. The formula line earns a mark.
• Elastic or inelastic: calculate the TOTAL E_k before and the TOTAL E_k after, then conclude: "inelastic, because kinetic energy is not conserved". A conclusion without both values earns nothing.
• A rebound changes the sign of the velocity: Δp = m(v_f − v_i) with v_f and v_i of opposite sign, so the two speeds add.
• Convert units first: g to kg (÷ 1 000), km·h^-1 to m·s^-1 (÷ 3,6).
• Safety features (crumple zones, airbags, seatbelts): they increase the time of the collision, and because F_net = Δp/Δt, the net force on the passenger is smaller for the same change in momentum.
• In a collision the two objects exert equal and opposite forces on each other (Newton's third law), so they receive equal and opposite impulses.

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Momentum and impulse exam questions Quiz on this topic

Terms and concepts to memorise and master

• Remember that Work is done on an object by a force acting parallel or at an angle θ to the displacement of the object
  W = FΔx cosθ
• Always start by drawing a free-body diagram of ALL the forces acting on the object

Remember the following aspects

• θ is the angle between the force and the displacement
• Work done by Normal is always Zero (θ is 90°)
• Work done by friction is always negative (θ is 180°)
• Work done can be positive, negative or zero

The net work done (W_net) can be calculated in three different ways

• W_net = W_F1 + W_F2 + …. (sum of work done by each force acting on the object)
• W_net = F_netΔx cosθ
• W_net = ½ mv_f² - ½ mv_i²
• ALWAYS LINK any two of these formulae, depending on the information given in the statement and what you need to calculate

• The net work done is zero (W_net = 0) if the object is stationary or move at a constant speed.
• If friction is the only non-conservative force acting on the object, then W_nc = W_f
• Use these formulae W_nc = ΔE_p + ΔE_k and mgh + ½ mv² = mgh + ½ mv² mostly when HEIGHT is involved, i.e. if the object moves vertically (up or down) or the object is on an inclined surface
• Use this formula mgh_i + ½ mv_i² = mgh_f + ½ mv_f² only when there is NO friction or any other applied force and also when height is involved
• Remember that in the formula P = W/Δt, W represents the work done by the force that develops the power
• Use the formula P_avg = Fv_avg if the speed of the object is given instead of time

Mark allocation

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Work, energy and power exam questions Quiz on this topic

Doppler effect: terms to memorise and master

• Use the Doppler Effect equation with the ± as given. It is the safest way to secure 1 mark.

Tips for choosing formula

Check the number of questions under Doppler Effect.

• If there is only ONE calculation, then the formula to use is f_L = (v ± v_L)/(v ± v_s) × f_s
• If there are TWO calculations, the one with MORE marks is the one to use the Doppler Effect formula for. The other calculation, usually for 3 marks, the formula to use is:
  • v = f × λ   Note that in this formula, v is the speed of sound in air, not the speed of the listener or the source of sound
  • f = 1/T
  The choice of the formula will depend on the question.

For the formula f_L = (v ± v_L)/(v ± v_s) × f_s

• Never use the same sign on both the numerator and the denominator. If + sign is used on the numerator, then − sign goes to the denominator and vice versa.
• If one, between the listener and the source of sound, moves TOWARDS another, the numerator will have the + sign and so obviously the − sign for the denominator. Use the word TOP to remember (TOP for numerator, TO for TOwards and P for Plus sign).

Applications

Memorize the applications of Doppler Effect in medicine and other fields:

• Ultrasound machine: to check the unborn baby for pregnant women
• Doppler flowmeter: to monitor the speed of blood

Redshift and blueshift

Explain Redshift and blueshift in terms of shift in spectral lines.

• Remember that Redshift proves to us that the universe is EXPANDING.

Where the marks are

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Doppler effect exam questions Quiz on this topic

Memorise and master the following terms

• Remember that positively charged object lost electrons and a negatively charged object gained electrons
• Remember that if two charged objects are allowed to touch each other, electrons will move from the object with a smaller electric charge to the object with a greater electric charge
• To calculate the actual charge on each object after separation, use the formula Q_new = (Q₁ + Q₂)/2 if 2 charged objects are involved or Q_new = (Q₁ + Q₂ + Q₃)/3 if 3 charges are involved and so on
• To calculate the number of electrons transferred

  First calculate the difference between the initial charge (before touching) and the final charge (after separation)

  Use the formula Q = n.q_e to calculate the number of electrons n. This number must always be negative.

• After stating Coulomb's law, use the formula F = kQ₁Q₂/r² for the next calculation
• After defining Electric field or Electric field at a point, use the formula E = kQ/r² in most cases where distance is involved. Otherwise use E = F/q if there is a charge at that point and you have been given or you have previously calculated the force
• Remember that there are only 3 possible shapes for the electric field pattern

Marks allocation

• State coulomb's law – 2 marks
• Formula for Coulomb's law – 1 mark
• Define Electric field or Electric field at a point – 2 marks
• Formula for electric field at a point – 1 mark
• Draw electric field pattern – 2 marks

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Electrostatics exam questions Quiz on this topic

Memorise and master the following terms:

Properties of series circuits

• Total resistance : R_T = R₁ + R₂ + …
  The total resistance increases as the number of resistors increases
• Current is the same through resistors in series: I_T = I₁ = I₂ = …
• Voltage is divided among resistors in series: V_T = V₁ + V₂ + …

Properties of parallel circuits

• Total resistance: 1/R_P = 1/R₁ + 1/R₂ + …
  The total resistance decreases as the number of resistors increases
• Current is divided among resistors in parallel: I_T= I₁+I₂+…
• Voltage is the same across resistors in parallel: V_T=V₁=V₂=…

Remember

• Remember the relationship between Current and resistance
  If the resistance increases the current decreases and vice versa
• If power is given, make use of the applicable formula for power
  P=VI,   P=I²R,   P = V²/R ,   or   P = W/Δt   in order to get either I, V or R
• For any resistor, always consider these 3 variables I, V and R
  If you are given 2 of them, calculate the unknown.
  Make use of the formula I = V/R in most of your calculations
• All resistors in an electric circuit are related in some sort
  • It is either they have the same current or same voltage or
  • They share the current or the voltage
• If you are asked to calculate the value of the internal resistance, use the formula
  V_Lost=I.r or ε = I (R + r)
• If you are asked to calculate the emf of the cell/battery, use the formula
  ε = I (R + r). Anyway, that is the only formula with emf from your data sheet.

Interpretation of basic graphs

Mark allocation

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Electric circuits exam questions Quiz on this topic

Question 9: Electrodynamics

• Know, memorise and master the following terms.

• Distinguish between a DC or an AC machine from given sketch diagram.
• List all components of an electric machine
• Graphs of output voltage or current of an AC generator

• Be able to perform calculations involving average Power

P_avg = V_rms·I_rms,    P_avg = I_rms²R,    P_avg = V_rms²/R

• Calculations are similar to the ohm's law calculations.

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Electrodynamics exam questions Quiz on this topic

Photoelectric effect

• Know, memorise and master the following terms

• State the dual-nature of light : Wave and particle
• Remember the order arrangement of EM radiations
  • In order of increasing frequency
    Radiowaves - Microwaves - Infrared - Visible light - Ultra violet - X-ray - Gamma rays (Remember RaMIVUX G)
• Remember the arrangement order of colours in a spectrum
  • Order of increasing frequency
    Red - Orange - Yellow - Green - Blue - Indigo - Violet. (Remember ROY GBIV)
• Remember that Photoelectric effect is a process, and as such it has three stages. The three stages are interdependent:
  You make use of information in stage 1 and 2 to find the unknown in stage 3. Similarly you use information in stage 2 and 3 to get information in 1. Or finally use information in 1 and 3 to get information in 2.
• Summary of what each stage represent and related definitions and formulae.
  From the Photoelectric Effect equation E = W₀ + E_kmax

• Tips for choosing formula
  Check the number of questions under Photoelectric Effect
  • If there is only ONE calculation, then the formula to use is E = W₀ + E_kmax
  • If there are TWO calculations, the one with MORE marks is the one to use the Photoelectric Effect equation (E = W₀ + E_kmax) for.
  • The other calculation, usually for 3 marks, use the applicable formula from the list below. The choice of formula is informed by the question and the data available
  • c = f × λ  or  c = f₀ × λ₀
  • f = 1/T
  • E = hf  or  W₀ = hf₀
  • E_kmax = ½ mv²
• Photocell

• The frequency of the incident light influences the speed of photoelectrons
• The intensity of the incident light influences the number of photoelectrons/current
• If the frequency of the incident light is increased
  • The speed (Kinetic energy) of the photoelectrons increases
  • The Ammeter reading (Number of photoelectrons) remains the same
• If the intensity of the incident light is increased
  • The speed of photoelectrons remains the same
  • The Ammeter reading increases
• Interpretation of a basic graph under photoelectric effect

• The x-intercept represents the threshold frequency f₀
• The y-intercept represents the work function W₀
• The gradient of the graph represents Planck’s constant

Line emission and Line absorption spectra

Line absorption spectrum

• Requirements: White Light - Cold gas - Triangular prism - screen
• White light contains all the seven colours of a light spectrum
• The particles of the cold gas absorb some of photons of the white light
• A photon corresponds to energy,
• Energy corresponds to frequency and
• Frequency corresponds to colour.
• These colours will be missing on the screen and dark lines will be seen throughout the spectrum

Line emission spectrum

• Requirements:
  (Other source of energy) - Hot gas - Triangular prism - screen,
• The particles of a HOT gas absorb energy (from the other source of energy) to move to a higher energy level.
• Particles fall back to their initial energy level by losing energy.
• The Energy lost is emitted in the form of light.
• The energy emitted corresponds to a frequency
• The frequency corresponds to a colour of light.
• On the screen, bright lights (lines) with colours corresponding to the energy emitted will be observed.

Marks allocation

Definitions to know

Say each one before you open it. These are the accepted exam wordings.

Practise the Photoelectric effect exam questions Quiz on this topic