CfE Higher Physics Unit 1Our Dynamic Universe
Our Dynamic Universe
Equations of Motion
Links to National 5: Speed, Distance and Time; Acceleration; Scalers and Vectors.
The Equations of Motion are used to determine a quantity relation to a moving object when the speed does not remain constant. There are three equations of motion that must be considered.
We use the acceleration formula from National 5 are re-arrange it slightly
Consider a moving object which does not start at rest and the speed is continually increasing.
We begin with Equation 1 in the Higher Physics form and square it. The brackets are then expanded.
Creating an information bank at the side of the page when doing a calculation allows for easier determination of which equation of motion to use.
s = Displacement (m)
u = Initial Velocity (ms-1)
v = Final Velocity (ms-1)
a = Acceleration (ms-2)
t = Time (s)
Motion Time Graphs
Link to National 5: Speed time graphs; Acceleration; Vectors
In Higher we must consider all aspects of motion when we display then in graphs – Velocity, Displacement and Acceleration.
As with National 5, the displacement travelled by an object can be calculated by using the area under the graph. Any area which lies below the x axis must be considered a negative value when calculating the total displacement.
The gradient of the line on a displacement-time graph is equal to the velocity of the object.
At Higher, acceleration will always be constant.
Bouncing Ball example
A – Ball is released from a height.
B – Ball reaches maximum velocity
C - Ball rebounds off the ground.
D – Ball reaches maximum height after rebound
When a velocity-time/acceleration-time graph falls below the x-axis, this can indicate that the object is slowing down OR that a change in direction has taken place. In both cases the magnitude value for velocity, acceleration or displacement will be negative.
Link to National 5 – Unbalanced Forces; Acceleration
Newton’s First Law states that an object will remain at rest or travel at a constant speed unless acted upon by an unbalanced force.
Newton’s Second Law states that the force applied to a mass is directly proportional to the acceleration of the mass.
Tension can be created by one object pulling another, or by an object hanging from a surface.
When one object is pulling another, more steps must be taken in order for the tension in the rope to be found. Take the example below to find the tension in the rope.
- Consider the total mass in order to calculate the acceleration of the whole system
- Consider the mass that comes after the tension rope ONLY. This mass is travelling with the same acceleration but is the mass creating tension.
Weight in a lift
When you step on a set of bathroom scales, the reading provided is actually the reaction force of the scales pushing back against your weight. When stationary the reaction force is equal to your weight. If you accelerate whilst standing on scales, the reading will be different.
An unbalanced force will act on the lift in the direction in which it is travelling. Weight will always be acting down; reaction force up.
Accelerating up in a lift
Accelerating down in a lift
Components of Force
If a force acts on an object at an angle, the force can be split up into horizontal and vertical components.
The forces are calculated using trigonometry (SOHCAHTOA)
Do not expect the horizontal and vertical components to add up to the original force being applied.
This same rule can be applied for masses sitting on a slope.
Component of weight down the slope = mgsinΘ
Component of weight into the slope = mg cos Θ
A box rests on a slope as shown in the diagram below.
The force of friction acting on the box as it moves down the hill remains constant at 1.2 N. Calculate:
(a)The perpendicular and parallel components of weight.
(b)The acceleration of the block down the slope.
Momentum and Impulse
Link to National 5 – Scalers and Vectors, Conservation of Energy
The conservation of linear momentum states that in the absence of external forces, the total momentum of a system before a collison is equal to the total momentum after the collison.
All moving objects have momentum – the number calculated is basically an indicator as to how easy or difficult it will be to stop the moving object.
The momentum is described as a product of an object’s mass and velocity. Take the following examples:
Mass = 5 kgMass = 10 x 107 kgMass = 0.01 kg
Velocity = 0.5 ms-1Velocity = 0.01 ms-1Velocity = 500 ms-1
So even though the trolley has a greater mass than the bullet and greater velocity than the tanker, it has the overall smallest momentum and would be easiest to stop!
Collisions and Explosions
Momentum is a vector quantity as it contains a velocity value – therefore direction is very important!!!! Always take an object going to the right as a positive velocity and to the left as a negative velocity. Take each object individually intially, then consider what is happening on either side of the collision. Consider the following examples:
Before – Separate; After – Separate
Before – Separate; After – Together
Before – Together; After – Separate (Explosion)
Kinetic Energy and Momentum
Even though kinetic energy and momentum are both linked to movement, they are not directly linked to each other. Consider the following examples:
The above boxes all have the same momenta but different kinetic energies. If the momentum and kinetic energy are the same it is entirely coincidental!!
Elastic and Inelastic Collisions
A collision can be deemed elastic or inelastic by whether the kientic energy of the system is conserved after a collision. Tackle this in a similar manner when completing momentum calculations – consider all objects’ energies individually, then before and after the collision, then the system as a whole.
Total Kinetic Energy Before Collision = Total Kinetic Energy After Collision
Collision is Elastic
Total Kinetic Energy Before Collision ≠ Total Kinetic Energy After Collision
Collision is Inelastic
In reality, all collisions are inelastic as some kinetic energy will be transformed into heat or sound energy.
Example so far: Calculate the velocity after the collision and determine whether the collision is elastic or inelastic.
Impulse is described as the length of time a force is applied to an object.
This impulse will cause an object’s speed to change, and therefore change the object’s momentum.
As the impulse in both statements is the same, we can finalse our equation:
Similar to a velocity-time graph, another value can be found from a force-time graph. The area under the force-time graph is equal to the impulse.
In these cases, time is usually a very small value and is often given in milliseconds.
A force-time graph can also show whether the object being hit is soft or hard, for example. Soft objects remain in contact for longer after being struck so therefore the force is not as sudden.
Links to National 5: Projectiles, Acceleration, Conservation of Energy
When an object is released, it will be classed as a projectile until it reaches the ground. Projectiles can travel horizontal or vertical. In Higher, we will look at projectiles launched at an angle, as well as horizontally and vertically.
The equations of motion are used to calculate certain features of a projectile, and certain rules remain the same. Units remain the same as before also.
Gravity will act as the ‘acceleration’ value for vertical movement = -9.8ms-2.
For projectiles launched with speed at an angle to the ground, the horizontal and vertical components of that speed can be found.
Projectiles launched at an angle will always follow a curved path. Split the path of the projectile in two – from start to highest point, then highest point to end – when looking at the vertical motion.
Horizontal motion remains constant throughout. When an object reaches maximum height, it will momentarily stop before falling back to Earth. This results in the final velocity for the first half/initial speed for second half of the journey to be constant. It will take half the total time to reach max height.
A golfer strikes a ball at an angle of 25° to the ground and with a speed of 60 ms-1. The ball lands 6s later. Calculate:
(a)The horizontal and vertical components of speed.
(b)The range of the ball
(c)The maximum height of the ball
Mass and weight are two things that can cause confusion in Physics. Mass is the amount of matter that an object consists of, whereas weight is a force pulling that object down to the ground. This force is caused by a gravitational pull.
There is always a gravitational pull between two masses – between two people for example. This additional gravitational pull between two objects is never felt as we are standing on the Earth – compared to a person, the Earth is MASSIVE!!
Newton devised an equation to calculate the attractive force between two masses that are a certain distance apart.
G = Universal Gravitational Constant (6.67 x 10-11 Nm2kg-2)
M1 and M2 = Mass of objects (kg)
r = Distance between the objects (m)
Example: What is the gravitational force between a man of mass 80kg and the Earth?
Comparing to W = mg = 80 x 9.8 = 784N
Albert Einstein was the first person to fully consider that travelling at the speed of light can alter space time – this was fully discussed in his Special Theory of Relativity. The theory states that, in reality, nothing of mass would be able to travel at the speed of light as the mass of the object would become infinitely large. Only photons of light can travel at this speed.
Theoretically travelling close the speed of light (90% of the value) can also have an effect on how an object is perceived by an observer – whether it be how large the object is or how long it takes to pass by.
An observer on Earth is looking at a space craft in space orbiting a planet. The observer and the space craft are in different frames of reference and the space craft is travelling close to the speed of light. To the observer, the time it takes for the space craft to make one orbit will appear much longer than the time it actually takes to orbit. This is known as time dilation.
Example: You leave earth and your twin to go on a space mission. You are in a spaceship travelling at 90% the speed of light and you go on a journey that lasts 20years. When you get back you will find that 46 years will have elapsed on Earth. Your clock will have run slowly compared to one on Earth, however as far as you were concerned the clock would have been working correctly on your spaceship, so for you only 20 years have elapsed. That is because the space craft and Earth are two different frames of reference.
An observer on Earth is looking at a space craft in space orbiting a planet. The observer and the space craft are in different frames of reference and the space craft is travelling close to the speed of light. To the observer, the length of spacecraft appears to be much shorter than the length it was when the space craft was on Earth. The spacecraft in reality has not gotten any smaller. This is known as length contraction.
Example: A spacecraft of length 270m is travelling at 0.83c (2.5x108) ms-1. It takes 35 minutes to orbit a distance planet. Calculate the length of the spacecraft and the time of orbit relative to an observer on Earth.
The Expanding Universe
The Doppler Effect
The Doppler Effect is the apparent change in frequency of a sound when the source of the sound is moving away or towards a stationary observer. The frequency of the sound does not actually change as only the source can change the frequency.
fo = Frequency heard by observer
fs = Frequency emitted by the source
v = Speed of Sound in air (340 ms-1)
vs = Speed of the source
What about the ± sign? This has got to do with whether the train is coming towards or away from the observer. Best way to remember:
- Coming towards Distance getting less Subtract
- Moving away Distance getting bigger Add
Example: A train is travelling towards a station at a speed of 17 ms-1. To alert passengers of its arrival, a siren is emitted with a frequency of 280 Hz. Calculate the frequency heard by the passengers waiting.
The universe is expanding – and it is doing so at an accelerated rate. This means that distance objects we can see (out with our Solar System) are moving away from us at a fast rate. This expansion cause the light we see from a distant star to actually be a different colour from the light being emitted. This is known as Redshift.
Redshift means that the light emitted from a distant object that is moving away from us appears to “shift” towards the red end of the spectrum. It does NOT mean that the light will turn red! the further away an object is, the more it “shifts” to the red end of the spectrum.
By how much the light has moved towards the red end of the spectrum can be determined with the following equation:
z is the red shift factor. It is a number (so no units) that determines how much the light has “shifted”. As the light being observed on Earth will always be longer than the light being emitted, you cannot get a negative redshift factor.
If the shift factor is negative, the light has actually moved towards the violet/blue end of the spectrum – this is known as Blueshift.
The redshift factor can also be used to calculate at what speed the object is moving away from Earth.
As redshift is a ratio between wavelength observed and wavelength emitted, it can also be used as a ratio between the speed of the object and the speed of light.
Example: A distant galaxy emits a photon of light with wavelength 570 nm. A student on Earth observes this photon as having a wavelength of 597 nm. Calculate the redshift value and the speed of the distant galaxy.
In 1929, the astronomer Edwin Hubble announced that other galaxies are moving away from us and the further a galaxy is from us the faster it is moving away.
Hubble developed an equation to help determine how quickly a distant galaxy is moving away from us.
v = Speed of the galaxy
Ho = Hubble’s constant (2.3 x 10-18 s-1)
d = Distance to galaxy
The Big Bang Theory
Certain areas of astronomy and astrophysics are still not widely known about and continued to be studied now. Scientists at institutes such as CERN and ITER continually work to understand why the universe was created in the way that it was.
Dark Matter and Dark Energy
‘It’s a fairly embarrassing situation to admit that we can’t find 90 per cent of the universe’–Astronomer B. Margon
Repeated measurements of the masses of galaxies lead to the conclusion that 90% of the universe is matter in a form that cannot be seen – dark matter.
Recent measurements of the expansion rate of the Universe found that the expansion is actually speeding up.
There is something that overcomes the force of gravity – dark energy.
Dark energy is now believed to make up most of the total content of the universe.
Temperature of Stars
As well as using the colour of light to determine how fast objects are moving away from us, the colour of light can also be used to determine how hot closer stars are.
Our own Sun is a relatively cool star in the grand scheme of things. The temperature of a star also has a link as to how bright (luminous) the star is also.
There are several sub categories of stars, including red giants and white dwarfs.