energy consepts

formulas needed for this topic

work and energy

• if a force moves something, we say the force does work. for example the following forces are doing work:
• -the force exerted by an electric winch pulls a car out of a ditch
• -the force exerted by an archers muscles when he draws a bow
• all these examples need something to drive them, unlike for example the force exerted by a table in holding up a book or the force exerted by a nail which holds up a shelf.
• THE WORK DONE BY A FORCE IS :
• WORK DONE = FORCE x DISTANCE MOVED IN THE DIRECTION OF THE FORCE
• (J) (N) (M)
• 

directions of force and displacement

• The tug in the diagram is pulling at an angle of the motion of the ship.
• so the definition of work done at an angle can be :
• Work Done = force x component of displacement
• in the direction of the force
• 

Example

• 
• The vertical component of the displacement is 300 sin 15
• Sin because it is opp and hyp
• Need to fing the height to be able to find the potential energy
• W = 900 x (sin15 x 300) = 270,000 sin15
• =70kj

e principle of cnservation of energy

• "ENERGY CANNOT BE CREATED OR DESTROYED- ONLY TRANSFERRED FROM ONE TYPE TO ANOTHER"
• Potential energy at A - Potential energy at B = 'loss of energy'
• the loss of energy is the WORK DONE BY FRICTION
• (eg)= friction / drag converted to heat energy
• friction did work on the ball
• work is the change in PE
• CHANGE IN PE = FORCE X DISTANCE
• 

Slide 6

• 
• Legenda: This is a diagram of the change from PE to KE. At the top of the ride the potential energy will be converted to kinetic energy at the bottom.
• Friction and drag cause energy to be transferred from a system and reduce the overall efficiency of the system
• some examples are:
• - a parachute jumper will reach terminal velocity. At this point his kinetic energy remains the same. However, he is losing potential energy as he falls and the height decreases. so where is the "lost" energy? well the parachute jumper has to do work overcoming air resistance.
• - a car braking can come to a stop. The kinetic energy of the car is seemingly "lost". However, the brakes have to do work stopping the car. Kinetic energy is transferred as heat in the brakes. ultimately, this will be transferred as heat to the surrounding air particles.

kinetic energy and potential energy

• KINETIC ENERGY-a moving object can do work on other objects in coming to rest. It possesses energy because of its motion.
• GRAVITATIONAL POTENTIAL ENERGY- an object in a raised position can do work on other objects as it descends. It possessed energy because of its height

Example

• 
• potential energy= m g h
• = 100 x 10 x 80
• =80000J
• the work done by friction= 80,000J
• (missing energy)
• it does not get converted into kinetic energy
• friction = w/d 80,000/ 400 = 200 N

common questions asked...

• 
• Legenda: a skier of mass 70 kg descends a slope inclined at 20 to the horizontal as shown
• (a) the gravitational potential energy lost by the skier
• need to find height to complete the formula
• sin20=opp/ hyp
• sin20=x/120
• x=sin20 x 120 x= 41.04m
• PE= 70 x 9.81 x 41.04
• PE= 28154.7
• (b) the kinetic energy gained by the skier
• KE = 0.5 x M x V^2
• KE = 0.5 x 70 x (21-6)^2
• KE = 0.5 x 70 x 405 KE= 14175J

...

• (c) state the principle of conservation of energy
• energy cannot be created or only transferred from one type to another
• (d) discuss your answers to b in terms of this principle
• energy was not conserved. the remaining energy goes to heat energy due to the friction between the skis and the ice.
• (e) calculate the mean resistive force experienced by the skier between A and B
• have to use an equation that links Joules and Newtons w = f x d
• f = w/d
• the missing energy is the work done by friction
• potential energy - kinetic energy
• 28154-14175 = 13979
• f = 13979/ 120 = 116.5N

assuming there are no resistive forces..

• Ep = mgh
• Ek = 1/2 m v^2
• if there are no resultant forces they will be equal
• on the second stage the m's cancel out
• 

Elastic potential energy

• 
• the spring constant , k , is defined by f= kx , where f is applied force and x the deformation (eg. stretch). calculating the work done by the varying force is like calculating the displacement from a velocity time graph: the work done is the area under the graph
• -the work done in stretching the spring W = 0.5 F X
• -substituting for F for F=kx W = 0.5 K X^2
• if the spring is allowed to relax, it can do work as it does so equal to the work done in stretching it, so the elastic potential energy is given by Ep = 0.5 K X^2

energy and power

• a force F acts on a body moving with a velocity V. F and V are in the same direction.
• P= WD
• T
• WD = F x D
• P= F x D D/T = SPEED
• T
• P=F x V

The efficiency equation

• We have said that energy is usually wasted as heat in the surroundings. This means that when a machine transfers energy, the useful output energy will be less than the total energy input.
• example:
• the work inut into the power station is 1100J but the increase in GPE is only 980J
• efficiency = 980/1100 x 100
• =89%
•