Higher Physics - Dynamic Universe (Gravitation, Special Relativity, Expanding Universe)

Projectile Motion

Projectile Motion

• Describes an object that is in freefall

• Only force acting on it is gravity (ignore air resistance)

Solving Projectile Motion Questions (Horizontal)

Will always be constant velocity so can be calculated by s=vt

Solving Projectile Motion Questions (Horizontal)

Will feature constant downward acceleration so can be calculated through v = u + at

Satellite Motion

Constantly falling towards Earth but moves fast enough that the ground falls away at the same rate

Newton’s Law of Universal Gravitation

Calculates the force experienced by an object in a gravitational field, through the equation F = Gm₁m₂ / r² where:

• F = Force

• G = Universal Constant (given on data sheet)

• m₁ = Mass of first object

• m₂ = Mass of second object

• r = Radius of orbit/distance between objects

Special Relativity

Theory developed by Einstein that describes how time and distance for objects moving at high speeds, in order to keep the speed of light constant.

NOTE - Relativistic effects only noticable above 0.1c (10% the speed of light)

Time Dilation

Where time passes differently for objects in motion relative to each other, and occurs when an object moves at speeds close to the speed of light, causing time to slow down for the moving object compared to a stationary observer. It can be calculated through the equation t’ = t/√(1 - v²/c²) where:

• t’ = Time measured by observer who object is moving relative to

• t = Time measured by observer in same frame of reference as object

• v = Velocity

• c = Speed of light

Length Contraction

Phenomenon in special relativity where an object's length appears shorter when moving at relativistic speeds, as observed by an observer at rest. This change can be calculated through the equation l’ = l√(1 - v²/c²) where:

• l’ = Length measured by observer who object is moving relative to

• l = Length measured by observer in same frame of reference as object

• v = Velocity

• c = Speed of light

Doppler Effect

The change in frequency of a wave in relation to the velocity of the emitting source, and can be found through the equation f = f₀( v / v ± v_s ) where:

f = Observed Frequency

f₀ = Source Frequency

v = Wave Speed

v_s = Speed of source

NOTE -

• In questions for sound, wave speed = 340ms^-1

• When source moving towards observer, subtract source speed (Towards/Take Away)

• When source moving away from observer, add source speed (Away/Add)

Redshift and Blueshift

When light comes from objects moving away from us, it gets shifted more to the red end of the spectrum, and when it moves towards us it shifts more towards the blue end of the spectrum.

This shift can be calculated using the equation z=(λ_observed - λ_rest )/λ_rest where:

• z = Shift value

• λ_observed = Observed Wavelength

• λ_rest = Wavelength at rest (actual wavelength/original wavelength)

NOTE - Positive z value means redshift, negative z value means blueshift

Recessional Velocity using Redshift

Can be calculated with redshift using the equation z = v/c where:

• z = Redshift/blueshift value

• v = Velocity

• c = Speed of light

NOTE - Must be at low speeds (below relativistic, <0.1c)

Hubble’s Law

Used to calculate the distance to objects using their recessional velocity, using the equation v = H₀d where:

• v = Recessional Velocity

• H₀ = Constant (found on data sheet)

• d = Distance

NOTE - Hubble’s Constant is 2·3*10^-18

Dark Matter

Existence is theorised by the fact that stars orbit around the centers of their galaxies faster than would be allowed for their observed mass, meaning that there must be matter invisible to us

Dark Energy

Redshift of galaxies shows that instead of slowing down due to gravitation, the rate of expansion of the universe is increasing, meaning that there must be another force pushing galaxies further apart

Black-Body Radiation

• Temperature of stars is related to the radiation emitted by that star, and the graph which that forms is a black-body radiation curve.

• Hotter stars have a shorter peak wavelength than cooler stars

Evidence for the Big Bang

• Redshift of Galaxies - (Hubble’s Law)

• Cosmic Microwave Background Radiation - Radiation left over from early stages of universe, expansion of the universe has caused wavelength to shift

• Olber’s Paradox - If the universe was infinitely massive and infinitely old, all the light in the universe would have reached Earth, making the night sky bright white

• Hydrogen, helium and other simpler elements are the most abundant in the universe because of how easier it was for them to form during the Big Bang