Forces

Scalar and vector quantities:
Scalar quantities have a magnitude, this simply says how big it is. Examples include mass, energy, temperature distance and speed. They all have a number and units associated with them.
Vector quantities have both a magnitude and a direction. Examples of these include all forces, displacement, velocity, acceleration and momentum.
The main point to see is with speed and velocity. They may both have a magnitude of 8 m/s, however, velocity will also have a direction. E.g. The bike had a speed of 12 m/s but it had a velocity of 12 m/s east.
Likewise, distance and displacement. The bike travelled a distance of 850 m but had a displacement of 850 m east.

Contact and non-contact forces:
Contact forces are forces which are in contact with the body that they are applying the force to. If you are pushing a shopping trolley around a shop, you are applying the normal contact force to it through the handle. Example of contact forces are: friction, tension and air resistance (drag).
In a non-contact force, there is no physical contact between particles. Examples of these are: gravitational force (weight), magnetic force (attraction or repulsion) and electrostatic force (attraction or repulsion).

Gravity, weight and gravitational field strength:
Gravity causes a force of attraction between objects with mass. The more mass an object has, the stronger the force is. We feel this force that gravity causes on Earth is weight. The gravitational field around Earth causes the force, weight, that pulls you towards the surface. If the person has more mass, the weight is bigger. If the planet had more mass, the weight is bigger.
We can calculate the size of this force using the formula: weight = mass x gravitational field strength of W = mg. The gravitational field strength is measured in N/kg and on Earth is is 9.8 N/kg. On different planets, the gravitational field strength is different. This means that although your mass is the same on Earth as it is on Mars, on Jupiter and even in the depths of space, your weight will vary wildly.
Don't forget that weight is a vector quantity so it will also have a direction. When you are on Earth, the direction of your weight is always towards the centre of the Earth.

Resultant forces and vector diagrams:
When there is more that one force acting on a body, you can cancel them out and replace them with one overall force, This is called the resultant force. As an example, imagine that there is a a boy pushing a trolley northwards (forces are vector quantities so have a direction) with a force of 15 N. Another boy is pushing on the same trolley with a force of 13 N in a southwards direction. The resultant force will be 3 N in a northwards direction.
A vector diagram allows us to plot accurately the forces on paper. Their magnitude is displayed as the length of the lines and their direction follows the direction of a compass. When plotted accurately, we can use the "missing" line as our resultant force.

Work done and calculating the energy transfer:
You need to know that the work done in moving an object is equal to the size of the force applied multiplied by the distance the object moves in the direction of that applied force. The formula is given as W = F x s
Note that instead of distance (scalar) we are using displacement S (vector). Force is in Newtons, displacement in Metres, and work done is in joules J. Obviously as the force applied increases or as the distance travelled increases, so will the work done or the energy used in doing the work.
Using this equation, we can give the unit of a joule a definition. If you push an item with the force of 1 N, for 1 m, then you will have used one joule of energy or 1 joule of work is done.

Forces, elasticity, springs, the energy stored in them and types of deformation:
If a force is applied to an object, you will see in later lessons that it will affect its motion. If, however, the object's motion is not changed, it can cause the object's shape to be changed. It can be stretched, crushed or twisted. If the object changes shape but returns to its original shape when the force is removed, it is said to be elastic deformation, such as gently pulling on a spring. If it permanently changes the shape, then it is said to me inelastic deformation, such as stretching the handles of a plastic carrier bag.
When you add a mass to the end of a dangling spring, the weight (force) will pull the spring down. This causes the spring to extend. Hooke's law shows that as the force applied increases, so does the extension, these are proportional right up to the limit of proportionality. Once this point has been passed, this relationship stops as we have moved into inelastic deformation. The relationship is connected by a spring constant which is specific to that spring. The formula is F=ke where k is the spring constant in N/m and e is the extension in m and the force is in N. Remember that this is the extension which is the extended length of the spring - original length of the spring.
When a spring is stretched, work has to be done to do it. We can link this to previous equations as we know that we add a weight (our force) and there is a movement (extenstion). We can then work out the amount of elastic potential energy stored in in our spring but we need to involve the spring constant as different springs will have different amount os energy sotred too. E_e = ½ k e². Elastic potential energy = 0.5 x spring constant x extension².
Note how similar this looks to the equation for kinetic energy: K_e = ½ m v²

Describing motion, distance and displacement:
This is a fairly simple concept, however, it is easy to get tripped up by it if you are not aware that distance is a scalar quantity and displacement is a vector. If you walk around a 400m running track and return to the start, your distance travelled will be 400m. As you have returned to the start, however, your displacement will be 0m.
Distance can be in straight lines, curves bends, zigzags etc, however displacement is a straight line from the starting point to the final point and the direction of travel.
Examples are: Distance = 27m, Displacement = 44m North west.

Speed and velocity:
Just like with distance and displacement, speed is a scalar quantity and velocity is a vector. Speed = distance/time whereas velocity = displacement/time. Both of these are measured in m/s but velocity has a direction added to it. Linking back to the running track analogy above, remember that velocity is in a straight line. The best thing to point out is that the Moon orbits earth at a speed of just over 1000m/s. The velocity of the Moon is 0m/s because its displacement will be 0m as it returns to the original point.

Acceleration:
Acceleration is a measure of the rate of change of velocity. This means that acceleration is also a vector quantity. Acceleration, or average acceleration, is how much the velocity of an object changes, divided by the time it took to change.
a = Δv/t
Acceleration is measured in m/s². If an object is slowing down, then it has a negative acceleration or is decelerating.
You can also this equation to find out the missing one from the following: initial velocity (u), final velocity (v), acceleration (a) and displacement (s)
v² - u² = 2 a s

Displacement-time and velocity-time graphs:
It is important with both of these types of graph to remember that time (s) runs along the x-axis. In a displacement-time graph, you can calculate the velocity by the gradient of the graph. The steeper the line, the bigger the velocity and if the line is flat (zero gradient) then the object has stopped. (If it is using distance instead of displacement, it is no longer a vector and you would get the speed rather than the velocity from the gradient).
In a velocity time graph, the gradient gives you the acceleration, if the velocity is in m/s and the time in s, then the acceleration is in m/s². The steeper the gradient, the higher the acceleration and if it is a negative gradient, the object is decelerating. If the line is flat (zero gradient), the object is travelling at a constant velocity. Finally, the displacement (distance travelled) can be calculated by working out the area under the graph.

Falling and terminal velocity:
When a body falls, we are interested only in the forces acting vertically up and down. Weight acts downwards (caused by gravity) and drag (also called air resistance) acting in the opposite direction. When a person jumps out of an aeroplane, they have not begun to fall so the only force acting on them in a vertical line is their weight, this causes them to accelerate downwards. As they gain velocity towards the ground, drag will increase in an upwards direction. When drag grows to be equal and opposite to the person’s weight and the forces are balanced, they reach terminal velocity. At this point, they are no longer accelerating and there is no resultant force.
When the person opens their parachute, the drag suddenly increases which unbalances the forces so they have a negative acceleration towards the ground (or they begin to decelerate) and the velocity reduces until the forces once again become balanced and a new, slower terminal velocity is reached. Many people think that when you open the parachute, you “shoot” back upwards but you simply slow down quickly. These forces, whether balanced or unbalanced can be shown on free body diagrams.

Newton's 1st law:
When you see the free body diagram for an object, if the resultant force is equal to zero, then the object will either carry on moving at its current velocity (both speed and direction) or if it wasn’t moving before, then it will remain still. We saw a part of this in the last component, when a person is falling, as long as their weight and drag are equal and opposite (balanced) they will continue to move at the same velocity (terminal velocity).

Newton's 2nd law:
As the force you apply to an object gets bigger, so does the object’s acceleration. This is one of easiest to understand concepts in all of physics. If you push a shopping trolley with a small force, it accelerates a small amount. If you shove the trolley with all of your strength, it will accelerate much more.
This can have values attached to it using the formula F = m a
or
Force (N) = mass (kg) x acceleration (m/s²)

Newton's 3rd law:
When objects interact, their forces are equal and opposite. You may have hear that “for every action, there is an equal and opposite reaction”. The best way to describe this is through a couple of examples, firstly if you run along the street, your shoe is pushing backwards along the pavement. At the same time, friction between your shoe and the pavement are pushing in the opposite direction which will propel you forward. Just to prove that point, imagine doing it on an icy morning, you still apply the force backwards but there is no reaction force because the ice prevents adequate friction and you fall or flail about like a cartoon character.
When a cannon fires a cannon ball, the explosion within forces the ball in one direction and the reaction force causes the cannon to move backwards in the opposite direction. Incidentally, referring back to the previous component, F = m a, the forces are equal and opposite (F) but the mass of the cannon ball is much smaller so it will accelerate much more than then cannon. The very large mass of the cannon means that it will only have a small acceleration (recoil).

Deceleration and the forces & energy transfers involved in braking:
When a car slows down, there has been a force applied to slow it down, this has come through the brakes. We can even work out the force applied through the brakes using F = m a. Remember that acceleration is a vector quantity so a negative acceleration is our deceleration. Energy is transferred in this process, the kinetic energy of the car has to be transferred to another energy store and that is the thermal energy store meaning that the brake pads, brake discs and tyres will become hotter. In fact, sometimes, a vehicle can suffer from “brake fade” which is when they become so hot, they no longer work efficiently.
The faster a vehicle is travelling, the longer it will take to slow down and the heavier it is, the longer it will take to slow down. These both, once again are linked to F = m a

Thinking, stopping and overall stopping distances:
Before we start, don’t fall for the mistake of replacing “distance” for “time”. We are only interested in the distance covered by a vehicle during these processes.
The thinking distance is the distance covered by the vehicle between the driver seeing the hazard and applying the brakes. This is very closely linked to their reaction time which is normally between 0.2 s and 0.9 s. If the driver was using a mobile phone, taking drugs, under the influence of alcohol or even trying to sort out an argument between children on the back seat, their reaction time is increased and so the thinking distance is also increased.
The braking distance is the distance travelled by the vehicle while the brakes are applied. This distance can increase if the tyres are worn or incorrectly inflated, the road is wet, icy or muddy, the vehicle has an excessive load/too much mass (linked again to F = m a or if the brakes are in need to repair.
Finally, we add these two distances together to produce the overall stopping distance. You need to be able to analyse data on these numbers and offer explanations as to why one of the two component distances has increased.

Momentum (HT):
Inertia is the tendency of an object to carry on doing what it is currently doing. That is either moving or not moving. The inertial mass is a measure of how difficult it is to change an object’s motion. A falling feather has a very low inertial mass and a fully laden container ship at maximum velocity will have a very high inertial mass. It can also be defined as the force/mass ratio.
Momentum is a property that all moving objects have, it can be calculated by multiplying the mass (kg) by the velocity (m/s). The units of momentum are kgm/s. The formula is p = m v
This is used to explain why very heavy objects moving slowly can be more difficult to stop than very small objects moving quickly. You can see that a 1 kg block moving at 20 m/s will have the same momentum as a 20 kg block moving at 1 m/s. Also note that momentum is a vector quantity so direction is very important.

The conservation of momentum (HT):
In a closed system (where energy does not enter or leave), momentum is conserved. This means that if a snooker ball hits another ball and stops instantly, the new ball will carry on with the exact same momentum as the first as 100% of the initial momentum is passed onto the second. Likewise in a collision, a ball moving to the left with p = 1.5 kgm/s hits a ball moving to the right with p = 1.5 kgm/s, the overall momentum before = 0 kgm/s so after the collision it must also equal 0 kgm/s. The balls may both stop or they may bounce off each other, either way, the overall momentum must remain the same. This is the conservation of momentum
In an explosion such as in a canon firing, the momentum before = 0 kgm/s so it must also =0 kgm/s after. This means that if the ball leaving the cannon has a momentum of 250 kgm/s to the East, then the cannon must have a momentum of 250 kgm/s to the West so that they cancel out. Note the link to the above component about Newton’s 3rd law of motion and as momentum is a vector quantity, you can apply the logic of a free body diagram to cancel out values.