Understanding Forces and Motion

Forces

• A force is a push or pull and can be either a contact force or a non-contact force.
• Contact forces necessitate direct physical touching and include normal contact force, friction, air resistance, and tension.
• Non-contact forces don't require direct touching, examples are magnetism and gravity.
• Forces are represented by vectors with magnitude (size) and direction.
• The resultant force is the net force on an object, found by adding individual force vectors, considering their directions.
• Balanced forces result in a resultant force of zero, meaning zero acceleration and constant velocity (Newton's first law).
• Scalar quantities have magnitude only, for example, speed.
• Vector quantities have both magnitude and direction, for example, velocity.
• Weight is the force due to gravity, calculated as mass (kg) × gravitational field strength (g, N/kg); on Earth, g ≈ 9.8 or 10 N/kg.
• Lifting an object at a constant speed requires an upward force equal to its weight.
• Work done (energy transferred) by a force: work done (J) = force (N) × distance moved (m).
• Gravitational potential energy (GPE) gained: GPE (J) = mass (kg) × g (N/kg) × height (m).

Springs and Deformation

• Forces can deform objects.
• Hooke's Law: Force (F) = spring constant (k, N/m) × extension (e, m). Valid for elastic deformation where objects return to their original shape after the force is removed.
• The spring constant indicates stiffness.
• Force and extension are directly proportional during elastic deformation.
• Direct proportionality is represented graphically by a straight line through the origin (0,0).
• Energy stored in a spring: E = 0.5 × k × e².
• Kinetic energy gained by an object released from a stretched spring is equal to the energy stored in the spring in an ideal system.

Moments

• Moment: a turning force, calculated as moment (Nm) = force (N) × perpendicular distance (m) from the pivot.
• The principle of moments: For equilibrium, clockwise moments equal anticlockwise moments about the same pivot.
• Gears: Using a small gear to turn a larger gear increases the moment produced.

Pressure

• Pressure is the concentration of a force: pressure (Pa or N/m²) = force (N) / area (m²).
• Liquid pressure increases with depth: pressure (Pa) = height (m) × density (kg/m³) × g (N/kg). Density of water is 1000 kg/m³.
• Gas pressure results from collisions of gas particles with surfaces.
• Gas pressure can be increased by adding more gas particles, reducing volume, or raising the temperature.
• Atmospheric pressure decreases with altitude because of lower air density.

Motion

• Speed and velocity are measured in m/s, but velocity includes direction.
• Speed/velocity = distance/displacement ÷ time.
• A distance-time graph's gradient represents speed/velocity.
• A velocity-time graph's gradient represents acceleration (m/s²).
• Acceleration = change in velocity ÷ time.
• Area under a velocity-time graph represents displacement; area below 0 m/s indicates negative displacement.
• SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
• AQA provides one SUVAT equation that can be used to calculate motion.
• To solve SUVAT problems, list known variables, identify the unknown variable, and choose the appropriate equation.
• For falling objects, acceleration = g = 9.8 m/s².

Newton's Laws

• Newton's First Law: An object's motion remains constant unless acted upon by a resultant force.
• Inertia: Tendency of an object to resist changes in its motion.
• Newton's Second Law: Force (N) = mass (kg) × acceleration (m/s²).
• Newton's Third Law: For every action force, there is an equal and opposite reaction force acting on a different object.

Practical Investigations of Newton's Second Law

• Use a trolley, track, pulley, and hanging masses to investigate the relationship between force and acceleration.
• Transfer mass from the hanger to the trolley when investigating Newton's Second Law, because the force accelerates both objects.
• Measure acceleration using light gates (photo gates).
• Plotting force against acceleration yields a straight-line graph, where the gradient is the total mass.

Stopping Distance

• Stopping distance = thinking distance + braking distance.
• Thinking distance doubles when speed doubles.
• Braking distance quadruples when speed doubles due to kinetic energy increasing by a factor of four (KE = 0.5mv²).
• Thinking distance is affected by distractions, alcohol, and drugs.
• Braking distance is affected by brakes, tires, road conditions, and weather.

Momentum

• Momentum is a measure of how hard it is to stop an object: momentum (kg m/s) = mass (kg) × velocity (m/s); momentum is a vector quantity.
• Total momentum is always conserved in a collision.
• M1U1 + M2U2 = M1V1 + M2V2 (before = after), where M is mass and U/V are before/after velocities.
• Pay attention to +/- signs for direction when calculating momentum.

Force and Momentum

• Force = change in momentum ÷ time (rate of change of momentum).
• Shorter time for momentum change results in greater force.
• Safety features such as seat belts, airbags, and crumple zones increase the time over which momentum changes, reducing the force felt.

Waves

• Waves transfer energy through oscillations or vibrations without transferring matter.
• Longitudinal waves have oscillations parallel to energy transfer (e.g., sound waves, seismic P-waves).
• Compressions (bunched particles) and rarefactions (spread particles) characterize longitudinal waves.
• Transverse waves have oscillations perpendicular to energy transfer (e.g., water waves, seismic S-waves, EM waves).
• Waveform: Graphical representation of a wave.
• Displacement: How far particles have oscillated from their original position.

Wave Properties

• Amplitude: Maximum displacement from the equilibrium position.
• Wavelength (λ): Length of one complete wave (meters).
• Time period (T): Time for one complete wave to pass a point (seconds).
• Frequency (f): Number of waves passing a point per second (Hertz).
• f = 1/T.
• Wave equation: wave speed (m/s) = frequency (Hz) × wavelength (m).

Wave Experiments

• A signal generator and ripple tank can be used to measure wave speed.
• To measure wavelength, measure the distance between 10 peaks and divide by 10 to get the average wavelength.
• Sound wave speed can be measured using a microphone connected to an oscilloscope to measure the time taken for reflected sounds.

Soundwaves

• Sound waves cause the eardrum to vibrate, converting vibrations to a signal for the brain.
• Human ear can hear frequencies between 20 Hz to 20 kHz.
• Ultrasound frequencies are above 20 kHz.
• Reflection and transmission occur when sound waves reach a boundary between two mediums.
• Ultrasound scans in medicine use reflected waves to create images.
• Sonar uses sound waves to map underwater environments.
• Seismic P-waves (longitudinal) can travel through liquids, but S-waves (transverse) cannot, indicating that Earth has a molten core.

Reflection

• Specular reflection: Reflection off a smooth surface like a mirror.
• Angle of incidence = angle of reflection (measured from the normal).
• Diffuse reflection: Scattering of light off a rough surface.

Electromagnetic Waves

• EM waves transfer energy through space.
• EM waves are produced when electrons lose energy.
• The higher the frequency, the more energy the wave carries.
• EM Spectrum order: Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
• Gamma rays are emitted by nuclei in nuclear processes.
• EM waves are absorbed by electrons.
• UV rays, X-rays, and gamma rays carry such high energy that they can ionize atoms, causing DNA mutations and cancer.

Uses of EM Waves

• Communications
• Cooking
• Heating
• Imaging
• Medical treatments

Refraction

• Refraction is the change in direction when light moves from one medium to another due to a change in speed.
• Light slows down and bends towards the normal when moving from air to glass.
• The angle of refraction is the angle between the refracted ray and the normal.
• All angles are measured from the normal.

Lenses

• Lenses are curved pieces of glass that refract light to either converge or diverge rays.
• Convex lenses converge rays.
• Concave lenses diverge rays.
• The principal focus is where parallel rays converge after passing through a convex lens.
• Focal length is the distance from the center of the lens to the principal focus.
• Image formation can be found by drawing rays from the top of the object.
• One ray goes straight through the center of the lens.
• The second ray goes parallel to the axis and then through the principal focus.

Image Characteristics

• Images formed by lenses can be diminished or magnified, and inverted or upright.
• When the object is very close to a convex lens, rays do not meet, and the image cannot be projected. A virtual image is formed instead, which appears to meet behind the lens.
• Virtual images can only be seen, not projected.
• Magnification of a lens is the ratio of its image height to the object's height.

Color Perception

• Color perception depends on the wavelengths of light absorbed or reflected by an object.
• Chlorophyll absorbs red light and reflects green light, giving leaves their colour.
• An object that looks blue reflects only blue light.

Black Body Radiation

• A black body is an object that perfectly absorbs or emits all light wavelengths.

Magnetism

• Permanent magnets have aligned molecules creating a magnetic field that can affect particles in other objects.
• The ends of magnets are called North and South poles.
• If free-floating, the poles align with Earth, similar to compasses.
• Iron filings are a useful tool to see magnetic fields.
• Magnetic field lines are complete loops and never touch.
• Magnetic fields travel out of the North pole and into the South pole.

Induced Magnets

• Induced magnets are metals whose particles align temporarily when placed within a magnetic field.
• Iron can be induced with North and South poles by magnets.
• Cobalt, nickel, and iron are magnetic elements, whereas aluminium and copper are not.
• Opposite poles attract, and like poles repel each other.

Electromagnetism

• A current flowing through a wire will produce its own magnetic field.
• The right-hand rule helps determine the field direction around a current-carrying wire.
• The motor effect occurs when a current-carrying wire is within a magnetic field, and a force is experienced.
• Force felt is calculated using F= Bill, where B is the magnetic flux density in teslas, I is the current in amps and L is the length of the wire.

Fleming's Left-Hand Rule

• Use your left hand, where the thumb is force, the first finger is the field, and the middle finger represents the current; each is positioned at 90 degrees to the others.
• Force is always perpendicular to both the field and the current.
• Measurement of the force can be completed using a balance due to Newton's third law (the reaction force).
• A mass measurement on the balance determines the amount of force present.

Electric Motors

• Electric motors use the motor effect, applying opposite forces on the ends of coils which results in turning.
• The current must be reversed every half turn to prevent the object from stopping vertically.
• A split-ring commutator is used to reverse the current every half turn in a DC motor.
• Increased current, a stronger magnet, or more turns on the coil can all result in a faster motor.
• Loudspeakers work due to a motor driving an speaker cone, creating sound waves in the air as it moves back and forth.

Electromagnetic Induction

• (Triple only)
• A wire moving through a magnetic field will have a current induced in it.
• This can also be called induced potential.
• The dynamo or generator effect occurs when a coil is turned in a magnetic field, thus inducing a potential.
• Power stations work this way, using steam to turn a turbine that turns the coil.

Dynamos

• To increase dynamo output, turn it faster, add more turns to the coil, or use a stronger magnet.
• Induced current also produces its own magnetic field resisting the rotation.
• Some dynamos are split in order to induce DC.
• Loudspeakers are a back-and-forth motor, while microphones are a back-and-forth generator
• A diaphragm moves back and forth around a magnet and induces a potential in the coil, creating a signal transmitted to the phone.

Transformers

• Transformers change voltage.
• Step-up transformers increase voltages before entering the grid to reduce energy loss during transmission.
• Electric power = voltage * current.
• In an ideal world, power input should equal power output.

Transformer Makeup

• Primary and secondary coils are wrapped around a soft iron core.
• The core has no electricity; it only facilitates magnetism.
• Electric current creates a wirelessly transmitted magnetic field.
• Transformers require AC, as a static magnetic field cannot create current.
• NP/NS = VP/VS; this equation can also be flipped depending on which terms represent primary (P) versus secondary (S) aspects of the transformer.

Space

• The solar system has a sun with 8 planets and an asteroid belt between Mars and Jupiter.
• Our galaxy is called the Milky Way.
• Stars form from dust and gas being attracted to each other through gravity, creating a nebula.
• The pressure from nuclear fusion and gravity pulling inward balance each other, allowing stability in stars.

Star Death

• At the end of a star's life, outward pressure forces the star to expand, creating a red giant (for smaller stars) or a red supergiant (for larger stars).
• A star then collapses, creating a white dwarf, and eventually a black dwarf.
• Large stars become red supergiants and go supernova when the nuclei fuse with extreme amounts of energy, releasing either a dense neutron star or a black hole
• Outer layers move away, forming new nebula from which new stars can be made.

Satellites

• Moons are natural satellites, while companies like Elon Musk's SpaceX create artificial satellites.
• Geostationary satellites orbit in a circle and are used for GPS and communication.
• Satellites are constantly accelerating towards Earth but do not crash because of their speed.
• Centripetal force leads to circular motion.
• Other satellites orbit elliptically at different speeds.
• Light from distant objects exhibits a red shift, suggesting that they are moving away.

Big Bang Theory

• Every direction has light that is red-shifted, suggesting galaxies are moving away from a central origin.
• Cosmic Microwave Background Radiation (CMB) is afterglow in the microwave spectrum of the universe's initial energy release, cooled down over time.