Rollercoasters and Relativity

• An objected lifted off the floor gains potential energy (often called gravitational potential energy.
• The added height gives it potential to do work when it falls.

POTENTIAL ENERGY = MASS x ACCELERATION x CHANGE IN HEIGHT

• The energy an object has because it's moving (if it's moving it's got kinetic energy)

KINETIC ENERGY = 1/2 x MASS x VELOCITY SQUARED

• The amount of energy in an electrical appliance. 

ELECTRICAL ENERGY = VOLTAGE x CURRENT x TIME

• The principle of conservation of energy says energy cannot be made or lost only changed from one form into another.
• Wind: the force of wind turns the blades of a wind turbine which causes a generator to spin and produce electricity:

- kinetic energy >> (wind turbines) >> kinetic energy >> (generator) >> electrical energy

• Water: water stored in reservoirs above a power station produces GPE. Flows through pipes to drive turbine:

- kinetic energy >> (turbine) >> kinetic energy >> (generator) >> electrical energy

• When a force moves an object, work is done on the object, resulting in a transfer of energy: work done = energy transferred

WORK DONE = FORCE x DISTANCE MOVED

• The rate of doing work. The greater the power, the more work is being done each second.
• Power is measured in watts (W) or joules per second (J/s)

POWER (W)  = WORK DONE (J)  / TIME TAKEN (s)

• If you swing a rubber ball attached to a piece of string in a horizontal motion at a constant speed the direction of the ball is always changing. 
• This means the velocity of the ball is also changing (velocity only) so the ball must be undergoing constant acceleration.

• Newtons law connects force with acceleration: force = mass x acceleration.
• The acceleration comes from a resultant force which acts on the ball keeping it moving in a circular path which is called a inward centripetal force.
• The same principle is applied the the moon and satellites in orbit around earth and earth around the sun. 
• The inward force is greater if: the mass increases, the speed/velocity increases, the radius of the circle decreases
• If the force suddenly stops (the string snaps) the object moves off in a straight line at a tangent in the circle. 

• Speed, acceleration, force and energy describe how a rollercoaster works. 
• The initial lift (lift hill) builds up GPE. 
• After reaching it's highest point, the rollercoaster starts down the first hill where gravity takes over and the GPE changes into kinetic energy.
• Gravity and the mass of the cars/passengers apply a constant downward force which makes the cars accelerate down the hill.
• The more GPE built in the initial lift, the more kinetic energy is produced for the rest of the ride and the faster the speed of the ride. 

• A rollercoasters energy is constantly changing from GPE to KE.
• Most GPE at the top of the first lift hill (lowest speed).
• As they drop, the GPE is being transferred into KE.
• The cars accelerate to reach their highest speed (max. KE) at the bottom of the slope.
• As the cars climb up the other sides, KE in transferred back into GPE.

• Einstein's theory of relativity is E = m x c x c
• The relativity theory refers to the idea that time and space are relative concepts.
• The Special and General Theories were proposed by Albert Einstein and extended the work of Isaac Newton.