Speed and Distance
Formulas: Speed = Distance/Time Average Speed = (u + v) /2
Distance Time Graphs
2) Flat sections= stopped
3) Steeper gradient=faster speed
4) Downhill=change in direction
5) Curves=acceleration or deceleration
6) Levelling off curve means its slowing down
Speed = Gradient = vertical/horizontal
Speed and Acceleration
Formula: Acceleration = Change in Speed/Time Taken
1) Gradient = Acceleration
2) Flat sections = Steady Speed
3) Steeper gradient = greater acceleration or deceleration
4) Area under any section of the graph is the distance travelled in that time
5) Curve = changing acceleration or decelleration
Velocity has a direction, e.g if a car turns around the speed is still 20 m/s but the velocity is then -20 m/s.
Mass, Weight and Gravity
Gravity is the force of attraction between all masses
Gravity gives an object its weight which is different from its mass
Mass is the amount of "stuff" in an object while weight is caused by the pull of gravity.
The weight of the object changes depending on the gravity taking effect.
Mass, Weight and Gravity Formula
weight = mass x gravity
Example: What is the weight, in newtons, of a 5kg chicken, both on Earth (g=10 m/s*2) and on the Moon (g=1.6 m/s*2)?
Answer: W = m x g
On Earth: Weight = 5 x 10 = 50 N
On the Moon: Weight 5 x 1.6 = 8 N
Six different forces:
1) Gravity or Weight always acts downwards2) Reaction force from a surface, usually acting straight upwards
3) Thrust, Push or Pull e.g by engine is the speeding up of something
4) Drag, Air Resistance or Friction is the slowing down of something
5) Lift due to an aeroplane wing
6) Tension is a rope or cable
1) Stationary object - all forces in balance
2) Steady horizontal speed - all forces in balance
3) Steady vertical speed - all forces in balance
If there is an unbalanced force you get acceleration, not steady speed.
4) Horizontal acceleration - unbalanced forces
5) Vertical acceleation - unbalanced forces
4 has a larger thrust than drag, 5 has a larger weight than drag.
Friction Forces and Terminal Speed
To travel at a steady speed, things always need a driving force to overcome the friction.
Friction occurs in three main ways:
a) Friction between solid surfaces which are gripping
b) Friction between solid surfaces which are sliding past each other
c) Resistance or "drag" from fluids
Moving objects can reach a terminal speed
1) When an object first set off they have much ore force acceleration them than resistance.
2) As the speed increases, the ristance also does.
3) This gradually reduces the acceleration until the resistance force is equal stopping the acceleration.
4) It will have reached its terminal velocity.
The terminal speed of moving objects depends on their drag
Forces and Acceleration
An unbalanced for means acceleraction, the size of the acceleration is determined by
F=MA - This is Newtons 2nd Law of Motion.
The overall unbalanced force is often called the resultant force
Generally, there are at least 2 forces acting on an object.
Factors affecting Stopping Distances
1) Thinking Distance
a) How fast you're going - need faster reaction if your travelling faster
b) Factors on yourself, e.g tiredness, drugs, alcohol
2) Braking Distance
a) How fast you're going
b) Weight of vehicle
c) Quality of brakes
d) Quality of grip ( road surface + tyres )
Speed affects braking distance more than thinking distance!
As the speed doubles the braking distance is times by 4.
Formula: Mass x Velocity Change in momentum = Force x Time
The greater the mass of an object and the greater its velocity, the more momentum the object has.
Momentum has size and direction - like velocity (but not speed).
It's the amount of time taken for a change in momentum that determines how big or small the force is. Therefore if someone's momentum changes very qucikly (like in a car crash), the forces on the body will be very large.
-The force of an object can be lowered by slowing the object down over a long down.
Safety features increases the collision time to reduce forces
1) Crumple zones crumple and change shape on impact, increasing the time taken to stop.
2) Seat belts stretch slightly, increasing the time taken for the wearer to stop.
3) Air bags also slow you down gradually.
These also reduce injuries by stopping people hitting hard surfaces inside the car.
Anti-Lock Braking System (ABS)
a) braes help drivers keep control of the car's steering when breaking hard
b) Ordinary brakes lock the wheels so they can't turn, which can cause the car to skid
c) Also give the car shorter breaking distances which could prevent a collision
Fact: crash tests have shown that wearing a seat belt reduces deaths in accidents by 50%
Work Done and Gravitational Potentional Energy
Formula: Work Done = Force x Distance
When a force makes an object move, energy is transferred and work is done. This energy can be used or wasted (lost as heat) but you can still say work is done.
Gravitational Potential Energy
GPE is the energy that something has because of its height above the groud. The energy to raise it is sotred and can be changed to kinetic energy if it falls.
Formula: GPE = Mass x g x height
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 will be.
Formula: Kinetic = 0.5 x mass x speed*2
If you double the mass, the K.E doubles, if you double the speed though the K.E quadruples due to the "v*2" in the formula.
This is linked to stopping distances and is the reason for the squared relationship between braking distance and speed.
Falling Objects and Roller Coasters
Falling Objects Convert G.P.E into K.E.
Formula: Kinetic Energy Gained = Gravitational Potential Energy Lost
0.5mv*2 = mgh
When a falling object reaches terminal speed its speed can't increase anymore, so its K.E doesn't increase. As the object wont change mass when falling they cancel out leaving
h = v*2 / 2g
This can be used to find the height something needs to fall from to reach a certain speed.
Roller Coasters Transfer Energy
a) at the top of a roller coaster the carriage has lots of G.P.E
b) as the carriage descends the G.P.E is transferred to K.E and the carriage speeds up
c) If you ignore any air resistance or friction between the carriage and the track the carriage will have as much energy at the top as it will at the bottom.
d) However in a real roller coaster these factors apply and it has to have enough kinetic energy to get rise up again.
Power is not the same thing as force, nor energy. Power is a measure of how quickly work is being done. Something is more powerful if it can transfer a lot of energy in a short space of time.
Formula: Work done / Time taken
Power is measured in Watts or Joules a second because 1 W = 1 J/s.
To find the power of something based on force and speed use:
Power = Force x Speed