Energy

WORK ENERGY THEOREM For an object that is accelerated by a constant force & moves in the same direction… Lets derive this…

Work-Energy Theorem The work done by the sum of the forces acting on a body is equal to the change in the kinetic energy of the body.

Kinetic energy exists whenever an object which has mass is in motion with some velocity. Everything you see moving about has kinetic energy. The kinetic energy of an object in this case is given by the relation: KE = (1/2)mv 2 m=mass of the object V=velocity of the object The greater the mass or velocity of a moving object, the more kinetic energy it has.

A fire truck of mass kg, travelling at some initial speed, has -2.9 MJ of work done on it, causing its speed to become 11 m/s. Determine the initial speed of the fire truck.

Text Book: pg 186 # 1,2,4-8 pg 188 #1-8 pg 226 # 5,6,12,13

Potential Energy What do we mean by your potential? It is what you are capable of doing, not what you are actually doing. Maybe you are getting a C+ in Physics, but you have the potential to get a B or even an A

Potential Energy What is the formula for Work? Work = F * d So if we are going to lift the object at a constant velocity, what is the work done? W = F G * h F FGFG h

Potential Energy W = F G * h But wait, what does F G equal? F G = m * g So… W = m * g * h F FGFG h

Potential Energy W = m * g * h Work is equal to the change in energy Potential energy due to gravity equals: Measured in Joules g = 9.80m/s² h Mass = m

Need a volunteer to lift an object

Gravity acts vertically, we will use ∆y for the magnitude of the displacement. The force applied to the object to raise it is in the same direction as the displacement & has a magnitude equal to mg therefore, W= (F Cos θ)∆h W = mg(Cos θ)∆h …where θ is 0

Gravitational Potential Energy (G.P.E) is a relative quantity in which the height of an object above some reference level must be known. The work done in increasing the elevation of an object is equal to the change in the G.P.E ∆Eg = mg∆h

Conservative & Non- Conservative Forces A force is conservative if the kinetic energy of a particle returns to its initial value after a round trip (during the trip the Ek may vary). A force is non-conservative if the kinetic energy of the particle changes after the round trip (Assume only one force does work on the object). Gravitational, electrostatic and spring forces are conservative forces. Friction is an example of a non-conservative force. For a round trip the frictional force generally opposes motion and only leads to a decrease in kinetic energy.

Potential Energy ΔE g = mgΔh This is only true for distances close to Earth, and where g is constant E g is not dependent on the path taken, only cares about height! Does not care about horizontal distance, cuz gravity doesn’t care Only care about height

Potential Energy Potential energy doesn’t only have to come from Height. Electrical potential energy Elastic potential energy Chemical potential energy

Text Book: pg.191 #1-6 pg. 194 # 1-5, 7