Section 1 d) Summary

Our Planet, the Earth, is located as the third planet from the Sun in the Solar System, one of billions of stars in the Milky way galaxy, which is one of billions of galaxies in the Universe.

Gravity, a force exerted by all bodies of mass, keeps celestial bodies in orbit around each other. It pulls bodies of mass back towards others and preventing them from moving far away, creating an orbit.

An orbit is a balance between the forwards motion of the object and the force pulling it inwards. Planets have almost circular orbits, whereas comets have elongated elliptical orbits. Moons and artificial satellites orbit planets in circular patterns.
Geostationary satellites have an orbit of 1 day, keeping it stationary over one area of land, and are useful for communications.

Stronger forces of attraction occur closer to the centre of a body of mass; because of this, planets closer to the Sun move faster, and comets move more quickly when they're closer to the Sun.

Orbital speed can be worked out through the following equation:

v= (2 x π x r ) / T

Section 1 d) Key Words

Artificial Satellite: A man made satellite, put into space by a rocket. Can orbit the Earth, or be put in orbit over another astronomical body.

Comet: Small lumps of icy rock that orbit the Sun. They have elliptical orbits and speed up when they're closer to the Sun as the gravitational strength is stronger.

Galaxy: A collection of billions of stars.

Gravity: The force exerted by all bodies of mass. Causes small bodies to orbit larger ones.

Milky Way: The galaxy we live in.

Moon: A natural satellite. Earth has one moon, known just as "the Moon", however other planets may have many more with individual names.

Orbit: The path one astronomical body takes around another, caused by the force of gravity.

Planet: A body of mass orbiting a star, e.g. the Earth orbiting the sun. It must be of a certain size to be classed as a planet, and have an almost circular, but usually slightly elliptical orbit.

Satellite: A body of mass that orbits another body of mass.

Solar System: The system of planets and comets around our Sun.

Star: A self-luminescent celestial body that produces energy.

Sun: The star at the centre of the Solar System.

Universe: A collection of billions of galaxies. Most of it is empty space. It's huuuuugeeeeeeeeeee

Section 1 d) Specification

1.32 understand gravitational field strength, g, and recall that it is different on
other planets and the moon from that on the Earth

All bodies of mass have a gravitational force that attracts other objects to them. Small bodies of mass, such as humans, have a tiny, immeasurable gravitational pull; but large bodies of mass such as the Sun are able to hold many other bodies of mass in orbit, such as the Earth. Earth has an approximate gravitational field strength of 9.8 m/s^2, but unless otherwise specified in the GCSE exam we should round it to 10. Larger planets such as Jupiter have more mass, therefore greater gravitational field strength: 24.8 m/s^2, whereas smaller bodies such as the Moon have such a weak gravitational field that they cannot have an atmosphere.

1.33 explain that gravitational force:

• causes moons to orbit planets
• causes the planets to orbit the sun
• causes artificial satellites to orbit the Earth
• causes comets to orbit the sun

Astronomical bodies orbiting others are constantly changing direction, as they travel in circles or ellipses; therefore there must be a force acting on them. Gravitational force from a larger body of mass pulls an object back towards it from it moving away.

The Sun pulls the planets and comets of the solar system inwards, changing their direction, which prevents them from travelling away from the Sun. The same principle applies for the Moon and artificial satellites orbiting the Earth, and the solar system orbiting in the Milky Way galaxy.

1.34 describe the differences in the orbits of comets, moons and planets

Comets orbit in a very elliptical shape, the Sun usually only at one end of the orbit, which are much longer than the orbits of planets as they travel a further distance. Comets move faster when closer to the Sun due to increased gravitational force. 
In contrast, Plants have relatively circular orbits, though they are slightly elliptical.
Artificial satellites orbiting the Earth can change their orbital period based on speed. Some have an orbital period of one day, and as a result remain stationary over the same area of land; these are called geostationary satellites.

1.35 use the relationship between orbital speed, orbital radius and time period:
orbital speed = (2 x π x orbital radius) / time period
v= (2 x π x r ) / T

To find the orbital speed, you first need to find the distance the object is travelling. We can do this using the same method you would find the circumference of a circle in maths: 2 x π x r. Then, to find the speed, the distance must be divided by the time period, so we get:
v= (2 x π x r ) / T

1.36 understand that:

• the universe is a large collection of billions of galaxies
• a galaxy is a large collection of billions of stars
• our solar system is in the Milky Way galaxy

Earth is a planet orbiting the Sun, the centre of the Solar System. The Solar System can be found as one of the billions of stars with planets orbiting them in our galaxy, the Milky Way. The Milky way is one of the billions of galaxies of the universe, most of which are unexplored.

Section 1 c) Summary

Forces
Balanced forces are forces that are equal is size and opposite in direction, and cause no change.
A force is a vector quantity; it has both size and direction.
Force is measured in newtons (N)

When forces are added together, they form a resultant force. Balanced forces always have a resultant force of 0N. If the resultant force is not 0N, the force is unbalanced, and the shape, speed, size or direction of the object will change.
There are different types of forces- they can be contact or non-contact.
Contact forces require particles to touch, for example friction, but non-contact forces act over a distance and don't require the particles to make contact to act, for example magnetic force.

Contact:

• Friction
• Drag
• Upthrust
• Tension
• Normal
• Air resistance

Non-Contact:

• Magnetic
• Electrostatic 
• Gravitational/weight
• Nuclear

Newton's laws of motion state that:
1. An object with balanced forces will not change in velocity.
2. A resultant force means acceleration
3. Every force has an equal opposing force.

The third law means that as you stand on the Earth, you are exerting a force on the ground, but the Earth exerts an equal force on you. This is called normal force.

As a boat travels through the water, a number of forces act on it. The upthrust from the water opposes the pull of gravity, and they are balanced. The force exerted by the boat as it moves through the water is opposed by water resistance, and above the water level motion is opposed by air resistance. These are both forms of drag; they are forces that oppose motion.

Friction is another form of drag, it happens when an object moves along a solid and is a force in direct opposition to motion.

Vectors and Scalars
Vectors and scalars are measures of quantity. A scalar is a measure of magnitude, while a vector is a measure of both direction and magnitude.

Terminal Velocity
Terminal velocity happens when the vertical force on an object are balanced. For example, a ball is dropped from a height. Initially, the ball will be accelerating because the weight is greater than the air resistance, but soon the weight and air resistance will become equal as the resistance builds up as velocity increases. Equal forces mean that the ball is no longer accelerating and is now travelling at a constant speed: it has reached terminal velocity. We can test terminal velocity using experiments with parachutes or sycamore seeds:

Sycamore seeds:
Seeds should be collected and the length of wing measured. They should be dropped and timed, and a graph drawn to show the relationship between length of wing and speed.

Parachutes:
Dropping same-weighted objects attached to parachutes of different sizes from the same height, and measuring the time it takes for the object to reach the ground. This is investigating the air resistance on the parachute, and should show that with increased surface area, the object will move more slowly.

Principle of Moments
If an object is balanced its clockwise and anticlockwise moments are equal.
If the moments are not equal, there is a resultant moment and the object will turn.

Examples of Balanced moments:

In the example above, we can clearly see the clockwise and anticlockwise moments are equal. On both sides, we multiply:

Force x Distance from pivot = Moment

50N x 2m = 100Nm

In this example, the blocks are in different positions and exert different forces, which must both have the same moments:

Force 1 x Distance 1 = Force 2 x Distance 2 

Moment 1 = Moment 2

50N x 2m = 100Nm

100N x 1m = 100Nm

The clockwise and anticlockwise moments are equal.

In the above example, a light beam is supported by two blocks at either end. The block placed in the centre exerts a force of 900N, which is spread equally between the two supports as they are at equidistance - the ratio is 1:1

450N + 450N = 900N

The sum of the force exerted by the supports must always equal the force exerted by the block. 

In this example, the block is closer to the left support. There is more force exerted on the closer support, and the distance can be split in a ratio of 1:2. We known there is more force on the closer support, so we know the force is distributed 2:1. We can divide 900N by 3, giving 300N to find the value of 1 in the ratio. 

900N / 3 = 300N

From this, we can put the values in the ratio to find the forces exerted on the supports

2 x 300N = 600N

1 x 300N = 300N

600N : 300N

Centre of Gravity

An object's centre of gravity is the point through which its weight acts. This point can be placed on a pinpoint and it will not overbalance because the weight acting on every side of it is equal. 

The centre of gravity can be found in a 2D object, for example a piece of paper in any shape, by suspending it and marking the vertical line below the point of suspension. If this is repeated, one point can be found where all the lines cross. This is the centre of gravity. 

Vehicular Safety

Forces and moment play a big part in ensuring driver and passenger safety in moving vehicles. Many safety features designed to prevent injury in the event of a crash use principles of momentum in their design. 

Force Felt = Momentum / Time

So while the momentum can't be altered, the time can be. Safety features increase the time over which momentum decreases, therefore decreasing the impact force. These include:

• Air Bags
• Seat Belts
• Crumple zones

Moving vehicles all have a stopping distance (made of thinking distance and braking distance) that is important to maintain to avoid dangerous collisions. The faster or heavier a vehicle is, the more momentum it has, making it more difficult to slow down in a short period of time and a short distance. If stopping distances are not maintained, it can lead to collisions and pile-up.

Stopping distances in cars can be affected by:

• Sobriety
• Old age
• Tiredness
• Inexperience
• Speed
• Mass of vehicle
• Brake quality 
• Weather conditions
• Road surface
• Tyre condition

Hooke's Law and Elasticity

Hooke's law states that the extension of an elastic object is proportional to the force acting on it. 

An elastic object is an object that can be stretched by a force, but will return to its original physical state once the force is no longer acting on it. However, all objects have an 'elastic limit', the point at which so much force has been applied that it loses elasticity and is unable to return to its original shape. After the elastic limit has been reached, the principles of Hooke's law are no longer relevant. 

Formulas

Weight = Mass x Gravity

Force = Mass x Acceleration

Momentum = Mass x Velocity

Force = Change in Momentum / Time taken

Moment = Force x Perpendicular distance from pivot

Section 1 c) Key Words

Acceleration: The rate at which the velocity of an object increases. A vector quantity.

Centre of Gravity: The point at which the mass of the object is equal in all directions; the point count be put on a pinpoint and it would not move as all the forces are balanced.

Drag: A force that opposes motion, for example friction or air resistance.

Elastic Limit: The point at which an elastic object is permanently stretched. Beyond this point Hooke's law cannot be applied.

Force: A push or pull on an object due to its interaction with another object, resulting in change of shape, speed, or direction.

Friction: A force opposing motion- happens between two solids e.g. a ball rolled on a carpet.

Hooke's Law: Hooke's law says that extension is proportional to force in an elastic object. As the force applied increases, the extension will increase proportionally.

Magnitude: Size

Mass: How much of an object there is; it has the same value anywhere in the universe

Momentum: How fast an object is going multiplied by its mass- its 'quantity of motion'

Newton's Laws of Motion: 1st law- balanced forces mean no change in velocity
2nd law- a resultant force means acceleration
3rd law- every force has an equal force acting in opposition to it.

Scalar: A quantity that has magnitude (size) but no direction. e.g. mass, distance, speed

Terminal Velocity: When the vertical forces on an object are balanced resulting in a constant speed and no acceleration.

Vector: A quantity that has both magnitude (size) and direction. e.g. weight, displacement, velocity, force

Weight: The force that gravity exerts on matter calculated by multiplying mass by gravity (which is 10 on Earth)

Section 1 c) Specification

1.9 describe the effects of forces between bodies such as changes in speed,
shape or direction

Forces acting on a body of mass can change its speed, shape or direction.

1.10 identify different types of force such as gravitational or electrostatic

All bodies of mass enact a force, known as gravitational force. Larger bodies of mass have more gravitational force than smaller ones, e.g. the Sun has gravitational force that is strong enough to keep the solar system in orbit; but a human doesn't have a strong enough gravitational field to attract any matter.

Forces can be contact or non-contact. Non-contact forces include drag, magnetic, electrostatic and gravitational; while contact forces involve direct contact and include friction, tension, normal, upthrust and air resistance.

1.11 distinguish between vector and scalar quantities

A vector has both direction and magnitude, e.g. acceleration
A scalar has only direction, no magnitude, e.g. speed

1.12 understand that force is a vector quantity

Force has both direction and magnitude; for it to be a force it must be acting in a direction, and it must be a measurable quantity (thus magnitude)

1.13 find the resultant force of forces that act along a line

The resultant force is the overall force acting in a direction on the object. This can be calculated by subtracting forces acting in opposite directions.

1.14 understand that friction is a force that opposes motion

Every action has an equal and opposite reaction- this is Newton's 3rd law of motion, which means that an object in motion will experience an opposite force in response, such as air resistance or friction.

1.15 know and use the relationship between unbalanced force, mass and
acceleration:
force = mass × acceleration
F = m × a

1.16 know and use the relationship between weight, mass and g:
weight = mass × g
W = m × g

1.17 describe the forces acting on falling objects and explain why falling objects
reach a terminal velocity

A falling object is affected by the vertical forces of gravity, which pulls it towards the Earth's centre of mass, and air resistance or drag, which works in the opposite direction of gravity. When it is falling and the forces are imbalanced-the force of gravity is greater than the air resistance- the object is accelerating. As the object increases in velocity, the air resistance increases, meaning that at a certain point, the drag will be equivalent to the gravitational force. When the force up = the force down, there is no acceleration, meaning the object will be falling at a constant velocity, known as terminal velocity.

1.18 describe experiments to investigate the forces acting on falling objects, such
as sycamore seeds or parachutes

Sycamore seeds:
Seeds should be collected and the length of wing measured. They should be dropped and timed, and a graph drawn to show the relationship between length of wing and speed.

Parachutes:
Dropping same-weighted objects attached to parachutes of different sizes from the same height, and measuring the time it takes for the object to reach the ground. This is investigating the air resistance on the parachute, and should show that with increased surface area, the object will move more slowly.

1.19 describe the factors affecting vehicle stopping distance including speed,
mass, road condition and reaction time

The stopping distance is increased by increased speed, as it takes space and time to decelerate;

Higher mass of vehicle means that when it is in motion it has more momentum, therefore requiring more space to stop with the same amount of force applied;

Wet or otherwise slippery roads decrease the friction with the wheels, making it more difficult to stop and increasing the stopping distance;

Reaction time affects stopping distance because it increases the time spent travelling at full speed and the distance travelled before the vehicle begins to decelerate. (Can be affected by tiredness, visibility, sobrerity, etc.)

1.20 know and use the relationship between momentum, mass and
velocity:
 momentum = mass × velocity
p = m × v

1.21 use the idea of momentum to explain safety features

Safety features in a car-
Seatbelt: Extends the time over which the person's body decelerates as it stretches, reducing impact force.
Crumple Zone: Force is exerted over a larger period of time and therefore reducing the impact force and damage to the person
Air bags: Change in momentum of the driver is spread out over a longer time, reducing impact force

1.22 use the conservation of momentum to calculate the mass, velocity or
momentum of objects

Momentum remains the same before and after a collision, so with certain variables given, mass, velocity or momentum can be calculated

1.23 use the relationship between force, change in momentum and time
taken:
force = change in momentum/time taken

1.24 demonstrate an understanding of Newton’s third law

Newton's third law is that every action has an equal and opposite reaction. This means that two bodies of mass interacting will exert forces on each other. For example, when a ball is dropped it will exert a force on the ground, and the ground will exert a force on the ball, leading to a resultant force that causes the ball to bounce up again. Another example is sitting on a chair: You exert a force on the chair, but the chair exerts an equal force back: supporting and holding you up.

1.25 know and use the relationship between the moment of a force and its
distance from the pivot:
moment = force × perpendicular distance from the pivot

1.26 recall that the weight of a body acts through its centre of gravity

The centre of gravity of an object is the point at which the mass is evenly dispersed at every direction from it. The centre of gravity of an object can be placed on a pinpoint and it won't overbalance due to uneven forces: it has a resultant force of 0 in every direction.

1.27 know and use the principle of moments for a simple system of
parallel forces acting in one plane

Moment = Force x Distance
Anticlockwise and clockwise moments must be equal, so for a pivot to be balanced the distance from pivot x force must be equal on both sides of the pivot.

You can use these rules and equations to work out different variables and balance different situations given.

1.28 understand that the upward forces on a light beam, supported at its
ends, vary with the position of a heavy object placed on the beam

Momentum is force multiplied by distance, so when the distance is altered, the force exerted must change to accommodate to the momentum, which remains the same (because clockwise and anticlockwise moment must be equal). If a heavy object is placed in the centre of a light beam that is supported at its ends, an equal force will be exerted on both supports; but if it is closer to support A than support B, more force will be exerted on support A.  This is like the previous, but upside down. It can be easier to imagine the force between the supports as the pivot and the supports as the weights.



1.29 describe experiments to investigate how extension varies with applied force
for helical springs, metal wires and rubber bands

Set up your apparatus so the object (spring, wire, rubber band, etc.) is suspended from a clamp on a weighted stand. Measure the length of your object before any force has been applied to find its natural length. Add a hanging mass and record the extension. Add an extra mass, record the extension and repeat, adding one mass at a time. Once you're done, repeat the entire experiment and record your results to draw an average and make your results more reliable. Graph the results to see how the extension varies.

1.30 understand that the initial linear region of a force-extension graph is
associated with Hooke’s law

Before the elastic object reaches its elastic limit, the quantity of force applied is proportional to the object's extension. This means that when it is graphed, it will produce a straight line. Hooke's law states that extension is proportional to force, which we can see clearly when we investigate the elasticity of different objects.

1.31 describe elastic behaviour as the ability of a material to recover its original
shape after the forces causing deformation have been removed.

Elastic objects and materials are able to be stretch when a force is applied, then return to their original shape once the force is removed.

Section 1 b) Summary

Distance-time graphs are used to show the change in distance over time: the displacement from the starting point. The velocity of an object can be determined from the gradient of one of these graphs. Negative points mean that the object is travelling in the opposite direction, and a negative gradient means the object is travelling back to the starting point.

Velocity-time graphs are used to show the change in velocity over time. The area between the line and the x-axis is used to calculate the distance travelled and the gradient is the acceleration. A negative gradient indicates deceleration and negative points mean the object is travelling backwards.

Experiments to investigate:

You could use ticker tape and a toy car on a ramp to plot a distance time graph of its movement. A mark is made on the tape at a regular interval, set by the user (e.g. every second). The distance between marks can be measured and the movement of the car plotted on a distance-time graph.

Another way of investigating the movement of an object, for example a tennis ball, is by dropping it or pushing it down a ramp and measuring the time it takes for the ball to reach a certain point after it begins moving. From this, the average speed can be calculated using the speed triangle.

Equations:

Velocity = Change in Distance / Change in Time

Acceleration = Change in Velocity / Change in Time

Section 1 b) Key Words

Acceleration: Measurement of how much the speed of an object increases over a length of time
Acceleration = Change in velocity / Time taken

Distance-time graph: A graph used to depict the displacement of an object from the starting point over time. Visual representation of velocity (the gradient)

Velocity-time graph: A graph depicting the speed of an object over time, also used to calculate acceleration by the gradient.

Section 1 b) Specification

1.2 plot and interpret distance-time graphs

Distance-time graphs show the change in time on the x-axis (which tells us how long the object took to travel a distance) and the change in distance on the y-axis (which tells us how far an object has travelled from the starting point).
Based on this, the gradient of the lines tells us the average velocity of the object (e.g. a straight horizontal line indicates a stationary object). The steeper the gradient is, the faster the object is travelling. A negative gradient means the object is travelling back closer to the starting point.

1.3 know and use the relationship between average speed, distance moved and
time:
average speed = distance moved / time taken
s = d / t

The relationship shown in this formula is represented clearly by this triangle:

This shows us that we can rearrange the formula to suit the information we have, and the information we wish to obtain.

1.4 describe experiments to investigate the motion of everyday objects such as
toy cars or tennis balls

You could use ticker tape and a toy car on a ramp to plot a distance time graph of its movement. A mark is made on the tape at a regular interval, set by the user (e.g. every second). The distance between marks can be measured and the movement of the car plotted on a distance-time graph.

Another way of investigating the movement of an object, for example a tennis ball, is by dropping it or pushing it down a ramp and measuring the time it takes for the ball to reach a certain point after it begins moving. From this, the average speed can be calculated using the speed triangle.

1.5 know and use the relationship between acceleration, velocity and time:
acceleration = change in velocity/time taken
a = (v-u)/t

Acceleration is the change in velocity divided by the period of time it took for the velocity to change.

By rearranging the equation, we can work out different variables in a situation, depending on the information we have and the information we need, similar to the speed triangle.

1.6 plot and interpret velocity-time graphs

The y-axis shows velocity, and the x-axis shows time. The gradient tells us the acceleration of the object, meaning that a positive gradient is accelerating, a negative gradient is decelerating, and a horizontal line means the object is travelling at a constant velocity. The steeper the gradient, the more quickly the object is increasing or decreasing in velocity. An object that is travelling at a constant speed, then comes to a sudden stop will have a horizontal gradient, followed by a very steep negative gradient.
We can work out the area beneath the line to find the distance travelled. A negative velocity means the object is travelling in a negative direction - the opposite direction (e.g. a car reversing)
(further information on v-t graphs here)

1.7 determine acceleration from the gradient of a velocity-time graph

Acceleration can be determined by calculating the gradient of a v-t graph, and represented with the appropriate units (e.g. if v is in m/s and t is in s, a will be m/s/s or m/s^2)

1.8 determine the distance travelled from the area between a velocity-time
graph and the time axis.

The distance travelled by an object from the starting point can be determined by calculating the area between the x-axis and the lines plotted on the graph.

As represented in the graph above, each of the differently coloured areas can be calculated and then added together to find the distance travelled by the object.
10 x 20 / 2 = 100
20 x 20 = 400
40 x 20 / 2 = 400
= 900 metres