Work, Energy and Power Kinetic  (work)  potential

Energy - Types Mechanical Energy: Energy due to position in a field force or energy due to movement Mechanical Energy: Energy due to position in a field force or energy due to movement Non-mechanical Energy: Energy that does not fall into the above category Non-mechanical Energy: Energy that does not fall into the above category

Energy – Flow Chart Energy Mechanical Kinetic Linear Rotational Sound Potential Gravitational Elastic Electric Magnetic Non-mechanical Heat Electromagnetic Chemical Nuclear

Kinetic Energy Equation

Potential Energy Equation

Work – Energy Principle or work done by a net force or net work done on an object

Energy Conservation The total energy is neither increased nor decreased in any process. The total energy is neither increased nor decreased in any process. Energy can, however, be transformed from one type to another AND transferred from one body to another, BUT, the total amount of energy in the process remains CONSTANT! Energy can, however, be transformed from one type to another AND transferred from one body to another, BUT, the total amount of energy in the process remains CONSTANT!

Conservative and Nonconservative Forces Conservative Force: A force such that the work done on an object by the force does not depend on the path taken, rather it depends only on the initial and final positions (gravitational, elastic, electric) Conservative Force: A force such that the work done on an object by the force does not depend on the path taken, rather it depends only on the initial and final positions (gravitational, elastic, electric) Nonconservative Force: A force such that the work done on the object by the force does depend on the path taken (friction, air resistance, rocket propulsion). A lot of times these forces generate heat or sound which are non-mechanical energies. Nonconservative Force: A force such that the work done on the object by the force does depend on the path taken (friction, air resistance, rocket propulsion). A lot of times these forces generate heat or sound which are non-mechanical energies.

Work – Energy Principle Redefined So if energy is conserved we can write it this way using mechanical and non-mechanical energies So if energy is conserved we can write it this way using mechanical and non-mechanical energies

Work – Energy Principle & Mechanical Energy Conservation If we ignore nonconservative forces (friction and the such), the implication is that no non- mechanical energies are present (heat, sound, light, etc) therefore… If we ignore nonconservative forces (friction and the such), the implication is that no non- mechanical energies are present (heat, sound, light, etc) therefore…

Mechanical Energy Conservation

Mechanical Energy Conservation with energy lost

Kinetic and potential energy convert to one another Frictionless Coaster : Total = Mechanical Energy

Work and Power Work – done when a force acts on an object in the direction the object moves Work – done when a force acts on an object in the direction the object moves Requires Motion and Force in one direction! Requires Motion and Force in one direction! Man is not actually doing work when holding barbell above his head Man is not actually doing work when holding barbell above his head Force is applied to barbell Force is applied to barbell If no movement, no work done If no movement, no work done He does work They do no work

Work Depends on Direction Continued… A. Force and Motion in the same direction B. The horizontal component of the force does work. C. The vertical force does no work on the suitcase. Force This force does work This force does no work Force Direction of motion Work and Power

Work Most of the time F is in the direction of d so θ = 0° and cos 0° = 1 so… Most of the time F is in the direction of d so θ = 0° and cos 0° = 1 so… Work is done by a force acting on a body! Work is done by a force acting on a body! Symbol: W Symbol: W Unit : J, joule Unit : J, joule 1 J = 1 Nm 1 J = 1 Nm

Work The simplest definition for the amount of work a force does on an object is magnitude of the force times the distance over which it’s applied: W = F x This formula applies when: the force is constant the force is in the same direction as the displacement of the object F x Symbol: W Unit : J, joule 1 J = 1 Nm

Tofu Almond Crunch When the force is at an angle x F  When a force acts in a direction that is not in line with the displacement, only part of the force does work. The component of F that is parallel to the displacement does work, but the perpendicular component of F does zero work. So, a more general formula for work is W = F x cos  F cos  F sin  This formula assumes that F is constant.

Power Power is defined as the rate at which work is done. It can also refer to the rate at which energy is expended or absorbed. Mathematically, power is given by: P = W t Since work is force in the direction of motion times distance, we can write power as: P = (F d cos  ) / t = (F cos  ) (d / t) = F v cos . F m  F sin  F cos  x

Power Power is the rate at which work is done or the rate at which energy is transformed. Power is the rate at which work is done or the rate at which energy is transformed. Symbol: P Symbol: P Unit: W, Watt Unit: W, Watt 1W = 1J/s 1W = 1J/s