Science EoY practice M4 Extended

Wave

A disturbance of energy that travels.

Wave-front

The front of a wave.

Longitudinal Waves

Vibrations/oscillations are in the same plane as the direction of travel.

Transverse waves

Vibrations/oscillations are transverse (at 90 degrees to) to the direction of travel.

Compression

Compressed part of a longitudinal wave.

Rarefaction

Spread out part of a longitudinal wave.

Energy

The capacity/ability to do work. The currency of physics. Energy is what we need to do work. Energy changed = work done.

Wavelength

The distance between two of the same parts of a wave. Eg. Trough or crest.

Amplitude

Height between the still point, and crest of a wave.

Frequency

Number of waves per second.

Period

The amount of time it takes to complete one wave cycle.

Equilibrium point

The center of a wave vertically.

Work

Force x distance moved.

Refraction

Where the wave changes velocity upon entering a medium. This causes light to change angle/direction when entering a medium.

Scalar quantity

A quantity with just size.

Vector quantity

A quantity with size and direction.

Wave propagation

How a wave travels.

Snell’s Law Equation

Vair / Vmedium = sin(angle of refraction) / sin(angle of incidence). This is also known as the refractive index.

Snell’s law Definition

Snell’s law states that the velocity of light in air divided by the velocity of light in a medium is equal to the sine of the angle of incidence divided by the sin of the angle of refraction.

Velocity (vector)

How fast and in what direction. Unit: meters per second (m/s or ms-1).

Speed (scalar)

Just how fast.

Inverse notation (x^-1)

x^-1 is just 1/x. For example, s^-1 = 1/s. ms^-1 = m/s.

Velocity Equation (distance/time)

V = distance traveled / time taken = d/t.

Frequency (f)

How many times per second. Unit: s^-1 or Hz.

Wavelength (lambda)

Symbol λ, unit: meters (m).

Wave Equation (velocity, frequency, wavelength)

Velocity = frequency × Wavelength (V = f * λ).

Period of wave (T)

Time for one oscillation of the wave.

Period-Frequency Relationship

Period of wave = 1 / frequency (T = 1/f).

Echolocation Distance Principle

In echolocation, the wave (pulse) travels to and from the object, so the actual distance to the object is half the total distance traveled by the wave.

Echolocation

Sending pulses of sound into a surrounding area, and based on how long these pulses take to return, the source can tell how far away objects are and where they are.

Wave Intensity

Intensity = Power / Surface area.

Power (in wave intensity)

Power = Energy / Time.

Initial Wave Intensity (Io)

The initial intensity of the wave.

Intensity at a distance (Ir)

The intensity of a wave at a point r distance away from the center.

Intensity Formula (2D wave)

Ir = Io / (2 * pi * r)

Intensity Formula (3D wave)

Ir = Io / (4 * pi * r^2). This uses the surface area of a sphere.

Wave Properties List

V=fλ, Oscillations, Wave fronts, Amplitude, Crest, Trough, Period, Frequency, Ray.

Ray

Rays travel in straight lines, unless affected by reflection or refraction.

Reflection

Incident angle = reflected angle (i=r).

Echo

A sound wave that is reflected.

Snell's Law (alternative form)

sin(i) / sin(r) = Velocity in medium 1 / Velocity in medium 2.

Index of Refraction (m)

sin(i) / sin(r) = C / V = m, where C is speed of light in vacuum and V is speed in medium. Wave speed is dependent only on the medium.

Total internal reflection

When the ray in the slower medium has such a large angle with respect to the normal that it reflects. Occurs if the angle of refraction is greater than the critical angle.

Diffraction

The process of light spreading out when it goes through a small aperture. Happens because light waves are made up of “point waves” that add up to create the next wave front, which curves slightly, making it spread out.

Electromagnetic radiation

A fluctuation of electric and magnetic fields.

Displacement (motion)

Distance and direction between two points. A vector quantity.

Distance (motion)

The distance travelled to get from one point to another. A scalar quantity.

Velocity from Displacement

displacement / time = velocity (vector).

Speed from Distance

distance travelled / time = speed (scalar).

Acceleration from Velocity

change in velocity / time = acceleration (vector).

Acceleration from Speed

change in speed / time = acceleration (scalar).

Acceleration Equation

A = (final velocity - starting velocity) / time, or A = (v-u)/t.

Gradient of a graph

Change in y / Change in x (Δy/Δx).

Displacement/Time Graph Gradient

Represents velocity.

Displacement/Time Graph Area

Has no meaning.

Velocity/Time Graph Gradient

Represents acceleration.

Velocity/Time Graph Area

Represents distance/displacement.

Newton’s First Law

An object will remain at rest, or in constant motion, unless an external force is applied. (Constant motion means keeping moving at the same velocity).

Newton’s Second Law

Force = Mass × Acceleration (F=mA or F=mΔV/t).

Newton’s Third Law

For every action there is an equal and opposite reaction.

Distance travelled (kinematics)

Length of trajectory, scalar.

Displacement (kinematics)

Distance measured in a straight line between starting point and ending point, vector.

Speed (kinematics)

Distance travelled / Time taken.

Velocity (kinematics)

Displacement / Time taken.

Acceleration (kinematics)

Change in velocity or speed / time.

Jerk

acceleration / time.

Projectile Motion Analysis

Separate motion into horizontal and vertical components.

Projectile Initial Horizontal Velocity

IV_horizontal = cos(θ) × IV. (IV = initial velocity, θ = angle to horizontal)

Momentum (P)

mass × velocity (P=mv). Units: kg ms-1.

Principle of Conservation of Momentum

The total momentum before a reaction is equal to the total momentum after the interaction. Applies to collisions and explosions.

Explosion (momentum)

Where 2 or more objects start from the same place. Example: a person stepping off a boat.

Elastic Collision

Kinetic energy is conserved.

Inelastic Collision

Kinetic energy is not conserved.

Gravity

One of the fundamental forces; a “non-contact” force originating from mass. It acts on mass to produce a real force.

Distance vs Time Graph Gradient

Δs/Δt = velocity.

Distance vs Time Graph Area

s*t, which is useless.

Velocity vs Time Graph Gradient

Δv/Δt = acceleration.

Velocity vs Time Graph Area

v*t

Instantaneous Velocity (Circular Motion)

Tangent to the circle at that point. Velocity is always changing direction, so not constant.

Angular Velocity (ω)

Measured in radians per second. (2π radians = 360 degrees).

Linear Speed and Angular Velocity Relationship

v = rω (v = linear speed, r = radius, ω = angular velocity).

Centripetal Force

Force that maintains circular motion, always directed towards the center of rotation.

Effect of Removing Centripetal Force

Object will travel at a tangent to the circle (its instantaneous velocity).

Centrifugal Force

The reaction force to the centripetal force.

Centripetal Force Equation (linear speed)

F = m*v^2 / r. (This is a form of F=ma, where v^2/r is the angular acceleration).

Centripetal Force Equation (angular velocity)

F = mrω^2. (Derived from F=mv^2/r and v=rω).

Period (T) in Circular Motion

The time it takes for one full revolution (seconds).

Frequency (f) in Circular Motion

The number of cycles per second (Hz).

Period-Frequency Relationship (Circular Motion)

T = 1/f, and f = 1/T.

Distance in One Revolution (Circular Motion)

Full circumference of the circle = 2πr.

Speed in a Circle (using Period)

v = 2πr / T.

Speed in a Circle (using Frequency)

v = 2πr * f.

Newton's Law of Gravitation

F = GMm / r^2. (F=Gravitational force, G=Gravitational constant, M=Large mass, m=Small mass, r=Distance between objects).

Gravitational Force and Centripetal Force Equality

mv^2 / r = GM*m / r^2.

Derived Velocity from Gravitation/Centripetal Equality

v^2 = G*M / r.

Kepler's Third Law (derived)

(4π^2 * r^3) / (G*M) = T^2. Implies r^3 is proportional to T^2.

Stokes' Law (Drag Force)

Fd = 6πηrv. (Fd=Drag force, r=Radius of the sphere, η=Fluid viscosity, v=Velocity of the sphere).