Ch. 6 Work & Energy – Handouts
Energy : is defined as the capacity to do work. Every change in the world is caused by energy and heat is always present when energy does work.
Work : When a force causes a motion to take place, work is said to be done. In physics work is W = F. d . cos ; where F is the force, d the displacement and is the angle between the force and displacement vectors.
There are three cases when no work is done, even if energy is expended
- when no force is applied
- when no motion or displacement takes place, for example pushing a brick wall
- when the angle is 900 ; for example carrying a bucket of water along a level ground.
Units of work is N.m = Joule (J) ; 1 J of work is done when a 1 N force moves an object for 1 m, the angle between them being equal to 00 or 1800. Maximum work is done when the force and displacement vectors are either in the same or exactly opposite directions. (Friction does negative work on the system as it always opposed the direction of motion). No work is done if Force and displacement are perpendicular to each other.
Law of conservation of energy : Energy can neither be created nor destroyed but only transforms from one form to another. Energy is measured in Joules.
When energy does work, some of it is lost as wasted heat and sound. Therefore the useful work output is always less than the energy used. This is the reason why electrical appliances or any kind of machines always get heated up and are never 100 % efficient. The best designed cars are only 30 to 35 % efficient.
There are two forms of mechanical energy : Total mechanical energy is always equal to M.E = P.E. + K.E
1. Potential Energy (P.E) : This is stored energy or energy possessed by a body at rest because of its location.
a. Gravitational P.E. : Water at the top of a fall, a skydiver, cat on a tree
The work done in raising or lowering an object in the gravitational field goes to changing its gravitational P.E.
W = F. d = Weight x height = m.g.h
b. Elastic P.E. : Energy in a stretched or compressed object; spring, rubber band
Elastic P.E = ½ k.x2 (k is spring constant; x is displacement of spring from mean position)
2. Kinetic Energy (K.E) : Energy possessed by a body due to its motion. If mass is doubled K.E. also doubles, if velocity is doubled, K.E. quadruples.
K.E = ½ mv2 (m is mass; v is velocity)
Power : is the rate of doing work or the rate at which energy is consumed. You use the same energy to walk and run up the stairs, but you need more power to run up the stairs than to walk.
Power (P) = Work (W) / Time (t) or P = Work / t (J/s)
Watt is the unit of power and is equal to 1 J /sec. A 40 Watt bulb used 40 J of energy in 1 sec. 1 kW = 1000 W. Electrical power is measured in W or kW. Electricity consumed is measured in kW-hour. KW-hr is a unit of energy and you are billed according to energy consumed. 1 kW-hr = 3.6 x 106 J.
Work Energy Theorem : When a net external force does work on an object, the K.E. changes from its initial value K.E.i to K.E.f; the work done is the difference or change in K.E.
W = K.E.f – K.E.i = ½ m.vf2 – ½ m.vi2
Work done by a gravitational field :
Wgravity = m. g. cos (hi – hf), is zero and Wgravity = m. g. (hi – hf)
Gravity is a conservative force and therefore work done by gravity is independent of the path taken, it depends only on the initial and final positions. If P.E. is totally converted to K.E. (no loss due to friction or air resistance) then ½ m.v2 = m.g.h or v = (2.g.h)1/2
When friction is present, work done depends on the path taken and not just on the initial and final positions. Frictional forces are non-conservative.