Work, Energy, and Power “It is important to realize that in physics today, we have no knowledge of what energy is.” - R.P. Feynman

F d F d rocket gains potential energy rocket has constant energy (circular orbit) F and d are parallel F and d are perpendicular F and d are parallel F d The Launch of a Rocket LIFTOFF!SPEED!ORBIT!

car gains kinetic energy car loses kinetic energy car maintains kinetic energy F and d are parallel F and d are perpendicular F and d are opposite Driving a Car SPEED UPSLOW DOWN‘ROUND A CORNER

Work and Energy Work and Energy are defined in a “circular” manner, meaning they are each defined based on the other. A measure of a change in the condition of matter Energy is transferred by doing work on a system ENERGY There is no such thing as pure energy. Only a transfer of energy, or a transformation of energy has meaning. Change in the energy of an object, or system (noun) Act of transferring energy (verb) WORK

Work force on an object displacement of an object Work depends on three things: angle between the force and displacement (force must cause the displacement) work is a scalar quantity, but can be positive, negative, or zero because it represents the amount of energy change. click for applet Units (metric or SI) FaFa PHYSICS FkFk FnFn FgFg d work is positive when 0˚<  < 90˚ work is negative when 90˚<  < 180˚ work is zero when  = 0˚ Which force does positive work? Which does negative work? Which does zero work?

Power Power is the rate at which work is done (or energy is used) Power can also be expressed in terms of force and velocity Units (metric or SI)

Potential Energy gravitational potential - depends on the position of mass in a gravitational field Potential energy is the energy of position of matter elastic potential - depends on the position of mass on an atomic scale g field massheight in joules spring constant position in joules

(translational) kinetic energy - depends on the motion of macroscopic objects (e.g. a car in motion) moving linearly Kinetic energy is the energy of motion of matter Kinetic Energy thermal energy - depends on the motion of microscopic objects (e.g. atomic vibrations). Often this energy is called heat. massvelocityin joules frictiondistance in joules click for applet work, dynamics, kinematics! WORK-ENERGY THEOREM

Conservation of Mechanical Energy click for animation Conservative forces (gravity, spring force) keep mechanical energy constant. Mechanical energy is the sum of kinetic and potential energy. Potential and kinetic energy may change, but the total mechanical energy does not change.

click for animation click for animation Non-conservative forces (friction, applied, normal, tension) change the mechanical energy, but total energy remains constant. Law of Conservation of Energy result of friction result of applied or normal or tension result of gravity or spring force

Conservation of Mechanical Energy Example A spring with constant 200 N/m is compressed 20 cm. It is released against a cart with mass of 0.5 kg that moves along a track without friction. What is the cart’s speed when it leaves the spring? What is the cart’s speed when it reaches the top of a 0.75 m high hill? At what height above the original release point does the cart come to rest?

Law of Conservation of Energy Examples (Assume there is zero air friction in these problems) A 75-kg Olympic ski jumper starts from rest and glides down a 30˚ incline 100-meter long. The track has surface friction. If the jumper leaves the track with a velocity of 28 m/s, what is the average force of kinetic friction on the skies from the track? In frustration, a physics student shoves a 1.2-kg textbook with a force of 14 newtons across a 0.5 meter wide desk that has no surface friction. If the book lands on the ground with a velocity of 5.2 m/s, how high is the desk above the ground? Honors: A 400-g wood block is attached to a spring. The block can slide along a table with coefficient of friction A force of 20 N compresses the spring 20 cm and the block is released. How far beyond the equilibrium position will the spring stretch?