Higher Physics Our Dynamic Universe

Scalar

A scalar quantity has only magnitude

Vector

A vector quantity has both magnitude and direction

Scalar quantities

* distance
* speed
* mass
* temperature
* energy
* power
* charge

Vector quantities

* displacement
* velocity
* acceleration
* weight
* force
* friction
* momentum
* impulse
* gravitational field strength

What are velocity-time graphs used for?

* To describe the motion of an object in detail
* Calculate the average velocity for a journey
* Calculate distances travelled and resultant displacement
* Calculate values for accelerations and decelerations

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Constant velocity

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Constant positive acceleration

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Constant negative acceleration

What does this show?

A ball thrown in the air

* decelerates upwards
* then briefly comes to a rest at the top
* then accelerates downwards

What is the gradient of a graph equal to

The acceleration

What does this graph show

A ball being dropped from a height and bouncing off the ground with the upwards direction taken as positive and downwards as negative

Describe each point on this graph

OA - The ball accelerates towards the ground. The velocity increases in the negative direction.

A - The ball hits the ground

AB - The ball changes direction

B - Leaves the ground

C - Top of flight

CD - The ball travels upwards and decelerates. The velocity decreases in the positive direction

(Process repeats)

In reality how is energy affected

In reality energy is lost as sound and heat in each bounce, as well as overcoming air resistance when travelling through air.

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Gradient of s-t graph is positive and object covers a larger distance each second (in the same direction)

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Gradient of s-t graph is positive and object covers a smaller distance each second (in the same direction)

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Every second the object covers the same distance in the same direction

Acceleration

The rate of change of velocity

Describe the motion of a bouncing ball thrown up in the air

A ball is fired up in the air with a positive velocity. It decelerates upwards to it’s maximum displacement, then accelerates **downwards** due to its weight (a=-9.8ms-2). When it reaches the ground it experiences a large, brief **upward** force which accelerates it upwards until it loses contact with the ground when the acceleration returns to a=-9.8ms-2

Describe motion of a ball dropped from a height

A ball is dropped from a height and falls towards the ground. When it reaches the ground it experiences a large, brief **upward** force which accelerates it upwards until it loses contact with the ground when the acceleration returns to a=-9.8ms-2

Equipment for an acceleration experiment

* cart
* card
* ramp
* ruler
* stopwatch
* light gate
* data logger

Method for acceleration experiment

1. Hold the cart at the top of the slope and release so initial velocity u = 0 ms-1
2. Use a light gate to measure the instantaneous velocity, v, of the card at the bottom of the slope in m/s. You will need to input the length of the card mask into the datalogger which can be measured using a ruler.
3. Measure the time between the cart being released and the light gate at the bottom of the slope using a stopwatch. This is t in seconds.
4. Use a = v-u/t to find acceleration, a, down the slope.

Comments on acceleration experiment

* Repeat the experiment at least 5 times to make the experiment more reliable (by reducing the random uncertainty)
* There will be reading error in the v and t as well as the random uncertainty

random uncertainty

max reading - min reading / num of readings

scale reading on analogue scale

\+/- half the least significant division of the scale

scale reading on digital scale

\+/- 1 in the least significant digit displayed

Newton’s 1st law of Motion

An object will remain at rest or constant velocity unless acted on by an unbalanced force

Newton’s 2nd Law of Motion

F=ma

Newton’s 3rd law of Motion

For every action there is an equal and opposite reaction

1 Newton is the unbalanced force which causes a mass of 1kg to accelerate at a rate of 1ms-2

Newton

Fun = ma

Equation for unbalanced force

Apparent W = W

apparent weight in a stationary lift

Apparent W = W

apparent weight in a constant velocity lift

Apparent W > W

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Apparent W = W + Fun

apparent weight in a lift accelerating upwards

Apparent W > W

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Apparent W = W + Fun

apparent weight in a lift decelerating downwards

Apparent W < W

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Apparent W = W - Fun

apparent weight in a lift decelerating upwards

Apparent W < W

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Apparent W = W - Fun

apparent weight in a lift accelerating downwards

Friction is a contact force which opposes motion

Friction

It can be minimized by smoothing surfaces or adding a lubricant such as oil

How can friction be minimized

For an object in free-fall, a constant speed is reached when the upward force on the object (air resistance) is balanced by the downward force on the object (weight)

Terminal velocity

As an object falls it accelerates.

As the speed increases, the air resistance on it will increase.

If it falls for long enough, the air resistance upwards will balance the weight downwards. When forces are balanced the speed is constant. This is the terminal velocity.

Describe the process of terminal velocity

A - initial acceleration = 9.8ms-2

B - first terminal velocity

C - parachute opened

D - second terminal velocity

E - ground reached

What happens at each point?

* Increasing velocity with decreasing rate of acceleration
* Initially there is an unbalanced force downwards as weight down is larger than air resistance upwards. As there is an unbalanced force, the object will accelerate as stated by Newton’s 2nd Law

Describe the motion between points A-B

* Terminal velocity
* Forces are balanced so as shown by Newton’s 1st law the object will move with a constant velocity

Describe the motion between points B-C

* Sudden decrease in velocity
* Large unbalanced force upwards provided by parachute’s large air resistance

Describe the motion at point C

* Second terminal velocity
* Forces are balanced so as shown by Newton’s 1st Law the object will move with a constant velocity

Describe the motion between points D-E

Tension is present when an object is being towed or suspended by a rope or coupling

Tension

Fv = Fsinθ

Vertical force at an angle

FH = Fcosθ

Horizontal force at an angle

Fdown_slope = mgsinθ

Force down slope

Energy cannot be created or destroyed, it can only be transformed from one type into another

Conservation of energy

* F unbalanced = rocket thrust - mg - friction
* The weight of the rocket decreases since g decreases as it moves further away from the Earth
* The mass of the rocket decreases as it uses up rocket fuel
* As it moves away from Earth, the friction forces due to air-resistance also decrease

Reasons why as a rocket rises the thrust remains constant but the acceleration increases

If the lift were not fully loaded

Describe a situation where a lift could have an upward acceleration greater than the max value without breaching safety regulations

The momentum, p, of an object is its mass multiplied by its velocity

Momentum

The total momentum of all objects before an interaction is equal to the total momentum of all objects afterwards in the absence of external forces

The Law of Conservation of momentum

Vector, RIGHT IS +, LEFT IS -

Is momentum scalar or vector

0kgms-1

Total momentum before an explosion

No kinetic energy is lost

Elastic collision

Kinetic energy is lost

Inelastic collision

* Newton’s 3rd law states that
* “Every action has an equal and opposite reaction”
* During explosions this tells us that objects will travel in opposite directions with the same applied force.
* This force gives rise to an acceleration in line with F=ma dependent on its mass and then a velocity after the contact.
* An equal and opposite force does not necessarily mean each object will travel at the same speed or have the same momentum, this is dependent on the mass

Newton’s Laws to describe collisions

If an object is accelerated by a force F, for a time t, the quantity Ft is known as impulse

Impulse

The concept of impulse is useful in situations where a force is not constant and acts for a short period of time

When is the concept of impulse useful?

The impulse of a force is equal to the area under a force-time graph **and** is equal to the change in momentum of an object involved in the interaction

The impulse of a force is equal to what?

When a human skull is brought suddenly to rest, a force acts upon the brain to change its momentum to zero. Without a helmet this occurs over a very short time interval.

* without helmet F1t1 = ()p1
* with helmet F1t1 = ()p2

But the change in momentum is the same so F1t1 = F2t2

Because the time to come to rest is much longer with a helmet, the average applied force will be much lower meaning less risk of brain damage

Explain in terms of impulse why a cycle helmet may reduce brain damage

1. Use a metre stick or measuring tape to measure the height of fall (displacement, s, in metres)
2. Use a stopwatch to measure the time (t), between dropping the ball and it hitting the ground in seconds
3. Ensure the ball is dropped so u = 0 m/s.
4. Use the equation s = ut + 1/2 at^2 to calculate acceleration, a

Experiment 1 to measure the acceleration of a falling object (using a stopwatch and a metre stick)

* The bigger the height the better to reduce impact of reaction time

Improvements for method 1 of measuring acceleration of a falling object

1. Use a metre stick or measuring tape to measure the height between the starting position of ball and the pad below (displacement, s, in metres)
2. Pressing the button on the electronic timer will release the ball (electromagnet turned off) and simultaneously start the timer. When the ball hits the pad below, the timer stops. The difference in these times will be time in seconds (t)
3. The initial velocity (u) is 0m/s
4. Use the equation s = ut + 1/2 at^2 to calculate acceleration, a.

Experiment 2 measuring acceleration of falling object (electronic timer)

A projectile has a constant horizontal velocity and a constant vertical acceleration simultaneously

Projectile

Satellites are in free fall around a planet/star

Satellites

The speed of light in a vacuum is the same for all observers

Speed of light in a vacuum

The clock would appear to run slow as the spacecraft is travelling at a relativistic speed, so time dilation would be experienced

If an observer on a planet was to view a clock onboard the spaceship, state whether it would run fast, slow, or normal compared to a watch on their wrist. Justify.

Length contraction

The length of a fast-moving object appears shorter to a stationary observer, what is this?

The change in observed frequency when a source of sound waves is moving relative to the observer.

Doppler effect

* When moving towards the observer, more waves are received per second and the observed frequency increases
* When moving away, fewer waves are received and so the observed frequency decreases

Doppler effect moving closer and further

The light from objects moving away from us is shifted to longer wavelength

Redshift

The redshift of a galaxy is the change in wavelength divided by the emitted wavelength

Redshift definition

Hubble and Lemaitre found that the further away a galaxy is from us it recesses at a greater speed

Hubble-Lemaitre Law

The Hubble-Lemaitre Law allows us to estimate the age of the universe.

Can be used as evidence to support the Big Bang Theory through evidence for the expanding universe

What can Hubble-Lemaitre Law allow us to do

v = Ho d

Equation for Hubble Lemaitre Law

The Hubble data shows that galaxies are moving away from us and the greater the distance from us, the faster they are moving away, i.e. Hubble Lemaitre Law

What does the Hubble data show?

The mass of a galaxy can be calculated if the orbital velocity of its stars around its centre are known

How can the mass of a galaxy be estimated

On closer observation, it does not appear that there is enough “normal matter” to stop galaxies from flying apart. To solve this problem, scientists have proposed that there is an additional type of matter holding galaxies together which cannot be seen - dark matter

Dark Matter

Not only is the universe expanding, but the expansion is accelerating. There is no obvious source of energy to cause this expansion but it has been termed dark energy

Dark Energy

* The temperature of stellar objects is related to the distribution of emitted radiation over a wide range of wavelengths
* The peak wavelength of this distribution is shorter for hotter objects than cooler objects
* Hotter objects emit more radiation per unit surface area per unit time than cooler objects

Temperature of Stellar Objects

The Big Bang Theory is based on the idea that the universe started from an exceptionally hot and dense state around 13.8 billion years ago and has expanded and cooled down over time

The Big Bang Theory

* The redshift of galaxies
* Cosmic Microwave Background Radiation
* Nucleosynthesis
* Olber’s Paradox

Evidence for the Big Bang

The “afterglow” of the Big Bang. This is radiation from the hot early universe whose characteristics closely fit those predicted by the expansion of space

Cosmic Microwave Background Radiation

* CMBR is almost identical no matter where you look
* CMBR comes from every direction of space (isotropic)
* CMBR corresponds to a temperature of around 3K, just a few degrees above absolute zero temperature
* CMBR radiation has a redshift z=1089, indicating that space itself has expanded
* Although CMBR is very low intensity, the universe is filled with it, so its total energy added up makes it the dominant radiation in the universe

CMBR features

Abundance of hydrogen and helium which agrees well with the Big Bang Theory

Nucleosynthesis

If the universe contains so many galaxies and stars then why is it dark at night?

The explanation suggests that light from these stars stretched as the universe expanded so it now arrives in the form of invisible infra-red radiation

Olber’s Paradox

Two observers moving at a constant speed observe the same laws of Physics

First basic postulate of Special Relativity