OCR Physics 21st Century (new) P4 - 'Explaining Motion'

Speed is just the Distance travelled in a certain time

Speed (m/s) = Distance travelled (m)/
Time taken (s) 

Example: A cat sulks 20 metres in 40 seconds. Find a) it's speed, b) how long it will take to skulk 75m.

a) speed = d/t =20/40= 0.5 m/s 
b) t =d/s  = 75/0.5 = 150s = 2 min and 30s 

The Speed of an object Normally Changes 

It's really rare for an object to move at a constant speed for a long period of time. So you need to find the average speed; this is what the formula tells you. 

Sometimes it's useful to find the 'instantaneous speed' or velocity (P.T.O)  

• Gradient = Speed
• Flat sections are where it's stationary
• The steeper the gradient, the faster it's going.
• 'Downhill' sections mean it's coming back toward its starting point.
• Curves represent acceleration and deceleration.
• A steepening curve mean it's speeding up (increasing gradient) -- it's accelerating.
• A levelling- off curve means it's slowing down (decreasing gradient) - it's decelerating.

Displacement-time graghs are almost the same idea as distance-time graphs apart from the gradient tells you about velocity.

Displacement can be positive or negative

Positive- one direction and Negative - the opoosite direction

When distance is given with a particular indication of direction, it's called displacement. Or 
the displacement of something is it's distance in a given direction, from it's starting point, at any particular moment in time.

Speed is just a number, but velocity has a direction too

The speed of an object is just how fast it's going - the direction isn't important. 
Velocity is sometimes a more useful measure of motion, beacuse it describes the direction. e.g. velocity =  30mph due north
Instantaneous velocity- 'its speed and direction at a given moment in time.  
You can also come across negative velocities, if a car turns around in the opposite direction.

Acceleration is how quickly you're speeding up

• is defintely not the same as velocity or speed
• is the change in velocity in a certain amount of time.
•  deceleration is just negative acceleration (if something slows down then the change in velocity will be negative).

THE FORMULA:
Acceleration (m/s^2) = Change in velocity (m/s)
   Time taken (s)

Example: A skulking cat accelerates steadily from 2 m/s to 6 m/s in 5.6 s. Find it's acceleration.
Answer: Change in velocity / time = (6-2) / 5.6 = 4/ 5.6 = 0.71 m/s ^2

• Gradient= acceleration
• Flat sections represent moving in a straight line at constant speed.
• The steeper the gradient, the greater the acceleration or deceleration
• Uphill sections (/) are acceleration in a straight line.
• Downhill sections (\) are deceleration in a straight line.
• The area under any section of the graph is equal to the displacement (distance) travelled in that time interval.
• a curve means changing acceleration.
• Negative velocity means that the object is travelling in the opposite direction.
• Speed-time graphs are similar to velocity- time graphs but ignore directions.

You can calculate acceleration from a speed- time graph too, but only if the direction of movement doesn't change. 

Forces occur when two objects interact
They work in pairs called 'partner forces' or 'interaction pair'

An object resting on a surface experiences a reaction force. 

Moving objects normally experience friction

• when an object is moving relative to another one, both objects  experience a force in the direction that opposes the movement - this is called friction.
•  Friction is a reaction force - it happens as a result of an applied force.
• The frictional force will match the size of the force trying to move an object, up to a maximum point - after this point of friction will be less that the other force and the object will move.
• There are three types of friction:
  a) Friction between solid surfaces are gripping
  b)Friction between solid surfaces which are sliding past each other
  c) Resistance or "drag" from fluids (liquids or gases)  

Arrows show the size and direction of forces

• The reaction of a surface - balanced forces
• Steady Speed - balanced forces
  If an object is moving with a steady speed the forces must be in balance (thrust, drag and reaction, weight) 

Resultant force is really important

The resultant force is the overall force acting on an object - the force  you get when you take into account (add up) all the individual forces and their directions. 
It's this forc e that decides the motion of the object - whether it will accelerate, decelerate or stay at a steady speed. 
Remember that 'accelerate' just means change velocity - and since velocity has both speed and direction, accelerating doesn't necessarily mean changing speed- it might just mean changing direction. For example, a car going round a corner is changing velocity (and therefore accelerating), even if it stays at a steady speed. 
So if there's a resultant force acting on an object, its speed or direction (or both) changes.

Acceleration - unbalanced forces 

If a car's engine exerts a bigger driving force (forwards) than drag counter force (backwards), the car will accelerate.
The bigger the resultant force, the greater the acceleration.
If the driving force was less than the drag , the car would slow down.
Note that the forces in the other direction (up and down) are balanced.

Momentum = mass x velocity

Momentum is mainly about how much 'oomph'  an object has - how hard it'd be to stop it moving.  The heavier the object is t, and the greater the velocity, the more momentum the object has. 

Momentum is a vector quantity - it has a direction and size.

A resultant force of zero means that a stationary object would stay still. If the object was moving, it stays at a constant velocity and constant momentum.
If the resultant force on an object is not zero, it's momentum changes in the direction of the force.  

The change in momentum depends on the force

When a resultant forces acts on an object, it causes a change in momentum in the direction of the force.The change of momentum it causes is proportional to the size of the force and the time it acts for:
CHANGE IN MOMENTUM = RESULTANT FORCE x TIME FOR WHICH THE FORCE ACTS

So, the bigger the force and the longer it lasts for, the bigger the change in momentum.
If someone's momentum changes really quickly, the forces on the body will be very large, and more likely to cause injuries.  

The greater the time for a change in momentum, the smaller the force.
So if your momentum changes slowly, like in a controlled breaking car in a car, the forces acting on your body are small and you're unlikely to be hurt.
In a collison, you can't really affect the change in momentum -whatever you do, the car's mass and its change in velocity will stay the same. However, the average force on an object can be lowered by slowing the object down over a longer time.  
Safety features in a car increase the collison time to reduce the forces on the passengers.

• CRUMPLE ZONES crumple on impact, increasing the time taken for the car to stop.
• AIR BAGS also slow you down gradually
• SEAT BELTS stretch slightly, increasing the time taken for the wearer to stop. This reduces the forces acting on the chest.
• CYCLE AND MOTORCYCLE HELMETS provide padding that increases the time taken for your head to come to a stop if it hits something hard.

"Work Done" is just "energy transferred"

When a force moves an object it does work and energy is transferred to the object. 

• Whenever something moves, something else is providing some sort of "effort" to move it.
• The thing putting the effort in needs a supply of energy (like fuel or food or electricity etc.)
• It then does "work" by moving the object -- and one way or another it transfers the energy it recieves (as fuel) into other forms. 
• Whether this energy is transferred usefully (e.g. by lifting a load) or is wasted (e.g. lost as heat), you can still say that work is done. 

  AMOUNT OF ENERGY TRANSFERRED (J) = WORK DONE (J)

• If energy is transferred then the object doing the work loses energy. 

WORK DONE BY A FORCE (J) = FORCE (N) x DISTANCE MOVED IN DIRECTION OF FORCE (m)

To find how much has been (in joules), you just multiply the force in newtons by the distance moved in metres. 

Example: Some hooligan kids drag an old tractor tyre 5m over flat ground. They pull with a total force of 340N. Find the work done.

Answer: W = F x d = 340 x 5 = 1700J 

Kinetic Energy is Energy of Movement
The kinetic energy of something depends on both its mass and speed. The greater its mass and the faster it's going, the bigger its kinetic energy. 
Kinetic Energy (J) = 1/2 x mass x velocity^2

Increase in K.E = Work Done, Just about
If work is done on an object, then the energy is transferred to that object, which probably is going to make it start moving or move faster.
An important concept of physics is that energy is always conserved. This means that you'd exoect the increase in an object's kinetic energy to be equal to the amount of work that's been done on it.
The problem is that some energy that's transferred is wasted as heat because of friction and air resistance. If you do 30J of work hitting a stationary ball then the ball's kinetic energy will be less than 30J because air resistance creates heat so...
THE INCREASE IN AN OBJECT'S K.E IS NORMALLY A BIT LESS THAN THE AMOUNT OF WORK DONE ON IT DUE TO SOME ENERGY BEING WASTED AS HEAT 
BUT  if the object is in space (i.e has no friction or air resistance acting on it) the K.E is equal to the work done on it.  

G.P.E is 'Height Energy'

• Gravitational potential energy is the energy stored in an object when you raise it to a height against the force of gravity.
• If you lift an object, it's G.P.E increases as it's raised.
• As an object falls, it's G.P.E decreases.
• You increase G.P.E by doing work.
• The increase in the G.P.E is equal to the work done by the lifting force in order to raise it's height. 

Change in G.P.E (J) = Weight (N) x Vertical Height difference (m)

Example: A 4000 N cow walks into a geyser, and is propelled 10 m upwards. Calculate it's change in G.P.E
Answer: Change in G.P.E = weight x vertical height difference = 4000 x 10 = 40 000J or 40 KJ  

Falling objects convert G.P.E into K.E
When something falls, its G.P.E is converted into K.E. So the further it falls, the faster it goes.
In practice, some of the G.P.E will dissipated as heat due to air resistance, but in exam Q it is usually ignored.

K.E gained= G.P.E lost