Dynamics and Space

Scalar quantities have magnitude (size) only. Scalar- distance, speed, energy, time, mass Vector quantities have magnitude and direction. vectors- displacement, velocity, acceleration, force, weight All vectors can be represented by a drawing an arrow. Vectors can be added by joining them tail to tip. The resultant vector (answer) starts from where the first vector starts from and finishes where the last vector finishes. It can be found by using a scale diagram or maths.

Distance (d) is the total distance travelled. It is a scalar.

Displacement (s) is the length measured from the starting point of a journey to the finishing point in a straight line. Its direction must be stated because it is a vector quantity. The direction can be given as left or right, up or down, as one of the compass points, as an angle or as a three-figure bearing (clockwise from North).

When we measure the speed of something, we are measuring the distance travelled each second (or hour).

d = vt

d = distance (m)   t = time (s)     v = speed (ms-1) 

Average Speed

Sometimes an object’s speed varies. For instance, a car travelling along a road will speed up and slow down due to traffic. In these situations, we calculate the average speed.

Average speed ( v ) = total distance travelled ÷ total time taken

Average speeds are measured over long time intervals. Long distances can be measured with a trundle wheel. Long time intervals can be measured with a stop watch. 

Instantaneous Speed

Instantaneous speed is the speed of an object at any given moment. In a car this is shown by the speedometer.

Instantaneous speeds are measured over very short time intervals. The instantaneous speed can be found by measuring the average speed over a very short time interval, usually less than 1 second. Short distances can be measured with a ruler, metre stick or tape measure. Short time intervals can be measured using a timer or computer connected to a light gate.

Instantaneous speed = length of vehicle (or mask) ÷ time taken to cut light gate

Velocity

Velocity is a vector quantity and requires a magnitude and direction. Velocity and speed have the same symbol (v) but different equations. The equation for velocity is,

s = vt

s = displacement (m)      t = time (s)         v = velocity (ms  ) 

The velocity will be in the same direction as the displacement.

Acceleration

The rate at which an object changes its velocity is called its acceleration. It is a vector and so has a direction as well as a magnitude.

Deceleration is slowing down or negative acceleration.

An object travelling at a constant velocity has an acceleration of zero.

a = acceleration (ms  )  u = initial velocity (ms  )  v = final velocity (ms  )

t = time (s)    Δv = (v-u) = change in velocity (ms  )

The gradient of the line is equal to the acceleration.

When velocity is not constant, d=vt cannot be used to calculate displacement. Instead use the equation,  s = area under v-t graph

Remember also, 

Area of a triangle = ½ x base x height

Area of rectangle = length x breadth 

Newton's first law of motion states that an object will remain at rest or moving at constant speed in a straight line if there are no unbalanced forces acting on the object.

Another name for the unbalanced force is the resultant force.                                                        Force is measured in newtons (N). 

Newton's second law of motion states that the acceleration of an object is directly proportional to the unbalanced force on it and inversely proportional to its mass.

 F = ma       F = resultant force (N) a = acceleration (ms-2) m = mass (kg) 

Friction is a rubbing force. The force of friction always acts in the opposite direction to which an object is moving.

The energy used to overcome friction is called Work Done.

Ew = Fd       Ew = work done (joules)(J) d = distance (m) F = resultant force (N) 

Weight is the force on an object due to gravity and is different on different planets. Mass is the amount of matter in an object and does not change.

W = mg         W = weight (N) m = mass (kg) g = gravitational field strength (Nkg  ) or (ms  )

The value of g depends on the planet. g = 9.8 Nkg-1 on Earth.

Newton's third law of motion states that every action has an opposite and equal reaction.

The action and reaction forces are known as Newton pairs.

Rockets move by burning fuel and releasing the exhaust gases behind them. From Newton's third law of motion, the action force is the force of the rocket on the gases, and the reaction force is the force of the gases on the rocket. It is the reaction force (called the thrust) which causes the rocket to move. 

The resultant force, F = T – W – Ff

The acceleration of the rocket can be found from, 

When an object is in free-fall through the air or water, there are two forces acting on it: weight and friction. The faster the object falls, the greater the friction. Eventually, the weight and force of friction will be balanced. The object will then fall at a constant speed, due to Newton's third law of motion. 

A projectile follows a curved path. Projectiles have both a horizontal and a vertical component of motion. In the horizontal direction their velocity is constant. In the vertical direction they accelerate downwards due to gravity. It is the combination of these motions which produce their curved path.

To solve problems involving projectiles, split the motion into two components (parts). Air friction can be ignored at National 5.

Horizontal

Constant velocity. d = v t where v  is the velocity in the horizontal direction.

Vertical

Satellites

Newton conducted a thought experiment. He imagined placing a cannon on top of a mountain and firing a cannonball horizontally. He knew that the cannonball would fall towards the ground at a constant acceleration and also that Earth was a sphere. He reasoned that if the mountain were high enough, and the cannonball fired fast enough, the cannonball would keep missing the earth and travel right around the planet.

This is what we now call a satellite. Satellites can be man-made such as weather satellites, communication satellites and the International Space Station. Examples of natural satellites are the planets orbiting the Sun, and moons orbiting planets.

Planets are large objects which orbit a star.

Moons are the natural satellites which orbit a planet.

Stars are enormous masses of very hot gas. The heat is created by nuclear reactions which take place in the star. They emit radiation, some of which is in the form of visible light.

The Sun is our nearest star.

An exo-planet is a planet orbiting a star other than the Sun.

A solar system is made up of a central star and all the planets and moons orbiting it.

Asteroids and comets may also orbit the star.

Galaxies are collections of billions of stars. They also contain gas and dust. The galaxy we are in is called the Milky Way.

The Universe

All the galaxies make up the universe.

The universe is the whole of space as we know it. It is not known what lies beyond the universe.

The observable universe is the part of the universe that we can see. The universe is 13.8 billion years old. That’s 13.8 x109 years old.

In the Big Bang Theory all the matter and energy of the universe was once an unimaginably dense mass. There was then an explosion that created the universe. The universe has been expanding from the explosion of this mass ever since.

We know that the universe is still expanding because the galaxies that we can observe are moving away from us. This is evidence for the Big Bang. 

The Light Year

Since distances are very large in space, astronomers often measure distances in light years. One light year (1 ly) is the distance light travels in one year.

speed of light = 300 000 000 ms-1 (or 3 x 10  ms  )

1 year = 365 x 24 x 60 x 20 = 31 536 000 s 

The Electromagnetic Spectrum

Radio, Microwaves, Infrared, Visible, Ultraviolet, X-rays, Gamma Rays 

All parts of the electromagnetic spectrum can be used in astronomy. Gamma ray telescopes pick up high energy events like supernova explosions. Young stars forming in cool dust clouds can be seen in infrared. The planets can be examined using visible light. Radio waves can be used to observe very cold hydrogen gas clouds in space.

The Visible Spectrum

White light is made up from the colours of the visible spectrum. These can be split using a triangular prism. The colours are Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROY G BIV). Red light has the longest wavelength and lowest frequency.

The complete visible spectrum is also known as a continuous spectrum.

When a gas is given energy, by either being heated or by an electric current passing through it, it gives out light at specific wavelengths. This forms what is called a line spectrum.

Each element has its own characteristic line spectrum. By examining the line spectra of stars, we can determine the elements they are made up of.

Benefits - Increased aviation safety; knowledge about the moon; gain knowledge about how Earth was formed; new materials made; new technology; carry out experiments in zero gravity; weather forecasting; environmental and climate change monitoring; navigation (GPS); spy satellites. Risks – astronauts being killed; expensive, especially if spacecraft fails or is destroyed. Re-entry When a satellite or spacecraft re-enters the Earth's atmosphere it will heat up to very high temperatures due to its high speed and air friction. Problems involving re-entry can be solved using the following equations:

Latent Heat

In reality, spacecraft do not experience the temperature rise you would expect. This is because they are designed to radiate heat when re-entering the Earth's atmosphere. A certain amount of heat energy still needs to be absorbed by the spacecraft and when the insulation gets too hot it begins to melt, boil and evaporate.

Heat shields are designed with coatings that deliberately vaporise. When a substance changes state the temperature of the substance remains constant whilst it is changing state. All of the heat energy that the heat shield is absorbing is going into melting or vaporising the coating, not into raising the temperature of the spacecraft. When a substance changes state from a solid to a liquid or liquid to a gas it requires energy. When a substance changes state from a gas to a liquid or liquid to a solid it releases energy. This effect is called latent heat.

The energy required to change the state of a substance (at its melting point or boiling point) is given by multiplying the mass of an object by its latent heat. 

The latent heat of fusion is used when going between solid and liquid.

The latent heat of vaporisation is used when going between liquid and gas.

E  = ml        E  = heat energy (J)   m = mass (kg)    l = latent heat (of vaporisation or fusion) (Jkg  )

giga (G) = 10  = 1 000 000 000 

mega (M) = 10  = 1 000 000

kilo (k) = 10  = 1 000

centi (c) = 10  = 0.01 

milli (m) = 10  = 0.001 

micro (μ)= 10  = 0.000 00

nano (n) = 10  = 0.000 000 001