Work, Power and Energy

Work - Definition The Scientific definition of the term work is quite different than what people commonly consider. Work is done on an object whenever a FORCE acts on the object, the object MOVES and the direction of the force & motion are PARALLEL.

Work - factors affecting The amount of work done depends on the amount of force and the distance the object moves while the force is applied.

Work - Formula The formula for calculating work is: W = F d W = the work done in Joules (J) F = the force applied in Newtons(N) d = the distance in meters (m)

Power - Definition defined as the rate at which work is done. Whenever we consider a “rate” time is usually involved. Power is the amount of work done in a certain amount of time. If work is done quicker then the power rating will be higher.

Power - Formula The formula for calculating power is: P = W / t where P = power in Watts (W) W = work done in Joules (J) t = time in seconds (s)

Work and Energy - Similarity Note that the units for Work and Energy are the same! These quantities are similar and can be used interchangeably in the formulas! Work W = F d or E = F d PowerP = W / t or P = E / t

Energy

is defined as the ability to do work.

Energy is defined as the ability to do work. If an object has the ability to apply a force on another object

Energy is defined as the ability to do work. If an object has the ability to apply a force on another object making the other object move (i.e. doing work)

Energy is defined as the ability to do work. If an object has the ability to apply a force on another object making the other object move (i.e. doing work) then we say the object has “energy”

wind light sound solar & many more Many Sources/Forms Examples include: chemical potential thermal (heat) nuclear gravitational potential kinetic electrical Energy - Sources/Forms

Since Energy is the “ability to do work” Each one of the above sources/forms of energy can somehow be used to apply a force causing work to be done.

Sample Problem To push a stalled Chrysler to the nearest service center a force of 380N is applied over the 2.3km distance taking a time of 23 minutes. Calculate: the work done and the power developed by the people pushing the junk car.

Sample Problem - solution F = 380N d = 2300m W = Fd W= (380N) (2300m) W= J

Sample Problem - solution W = J t = 23 min t = 1380sec P= W / t P= (874000J) / (1380s) P= 633 Watts

Work/Energy Theorem When work is done on an object the energy the object has is “changed.” Work causes a change in energy! The amount of work done is equal to the change in energy. or simplyW =  E

Kinetic Energy (E k ) This is the energy an object has because of its motion. An object in motion could “hit” another object and do work on it “ability to do work” = “energy” The amount of E k depends on the mass of the object and its speed.

Kinetic Energy (E k ) Formula: E k = 1 / 2 m v 2 E k = kinetic energy (in Joules (J)) m = mass of the object (in kg) v = speed of the object (in m/s)

Gravitational Potential Energy (E p ) This is the energy an object has because of its position above the earth. An object could “fall” on another object and do work on it “ability to do work” = “energy” The amount of E p depends on the mass of the object and its height above the earth.

Gravitational Potential Energy (E p ) Formula: E p = m g h E p = potential energy (in Joules (J)) m = mass of the object (in kg) g = acceleration of gravity (in m/s 2 ) h = height (in m)

Gravitational Potential Energy (E p ) Note – the zero height can be set at any convenient location We are actually calculating a “relative” potential energy The potential energy can be calculated above or below that height. E p can be negative if the height is below the selected zero point. “Changes” in E p are most significant

Conservation of Energy Energy cannot be created or destroyed! The total amount of energy you start with will always be the same as the total amount of energy you end up with. Energy can however be changed from one form to another Energy changes are done quite frequently in our society.

Conservation of Energy For example when an object falls it loses some E p while it gains some E k In fact the amount of E p lost will be equal to the amount of E k gained (unless some energy is lost to the surroundings.) Most of the “devices” we use are actually energy “converters.”

Energy Conversion Devices Examples: BBQ (chemical potential ==> heat) pizza oven (electrical energy ==> heat) Car (chemical potential ==> to heat, light, sound, and kinetic energy) Lights (electrical energy ==> light) TV (electrical ==> light and sound) Human (chemical ==> heat, sound...)

Example Problem A 12kg object is dropped from rest at a height of 73m above the earth. Calculate the speed of the object as it passes a point that is 26m above the earth and then calculate the speed the mass hits the ground with.

Example Problem - solution At the top the object has no kinetic energy but it has Ep so its total energy is just the amount of Ep it has At the top (at a height of 73m) E total = E k + E p = 0J + mgh = 0J + (12)(9.8)(73) E total = 8585J

Example Problem - solution At a height of 26m The object is now moving and so it has both potential and kinetic energy E total = E k +E p = 1 / 2 m v 2 + mgh = (0.5)(12)v 2 + (12)(9.8)(26) E total = 6v J

Example Problem - solution We know the total energy (from above) which doesn’t change (because of the conservation of energy) and so: E total = 6v J E total = 8585J= 6v J 5527J= 6v 2 921= v m/s = v

Example Problem - solution At a height of 0m Object is moving and so it has E k E total = E k +E p = 1 / 2 m v 2 + mgh = (0.5)(12)v 2 + 0J E total = 6v 2 + 0J But we know the total energy is still 8585J and so:

Example Problem - solution E total = 8585J= 6v = v m/s= v so the object would strike the ground moving at 37.8m/s