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The story so far…. Distance (displacement) is change in position (m) Velocity is change in position with time (m/s) Acceleration is change in velocity with time (m/s 2 ) Mass is a measure of how much matter (kg) Force is needed to accelerate an object (N)
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The story so far…. • Distance (displacement) is change in position (m) • Velocity is change in position with time (m/s) • Acceleration is change in velocity with time (m/s2) • Mass is a measure of how much matter (kg) • Force is needed to accelerate an object (N) • Momentum is a measure of inertia in motion (kgm/s) • Force x time changes momentum (impulse) • Next idea is Work and Energy
Boston Marathon • Boston Marathon is more than 26 miles. • It starts in Hopkinton (500 ft above sea level) and finishes in Boston (at sea level). • World class runners finish in 2 hours and 10 minutes. • It takes a jogger 4 to 5 hours to finish. http://www.bostonmarathon.org/BostonMarathon/CourseMaps.pdf
How much energy (or work) does it take to run the Boston Marathon?
energy joule work potential energy kinetic energy law of conservation of energy Describe work and energy. Calculate potential energy. Calculate kinetic energy. Apply the law of conservation of energy to explain the motion of an object acted on by gravity. Objectives and Vocabulary
Definitions of Work and Energy • Work is the measure of the energy (or fuel) needed to do a job • Energy is a quantity that measures the ability to cause change in a physical system. • Energy and work are closely related. • Our bodies are not a reliable measure of the work needed to job • Our bodies are not efficient machines • You think you are doing work when you really aren’t from a physics point of view.
Key Work Ideas • Work = force x displacement • Force and change in position must be in the same direction for work to occur. • if the force and displacement are in the same direction work is positive • if the force and displacement are in opposite directions work is negative • if the force and displacement are at right angles, there is no work • Unit of Work = N m = Joule (J)
Force and Displacement at an Angle • If the force and displacement are at an angle, work equals F * d * cos , where is the angle between the force and displacement. Example: If the force is 20 N, the displacement 5 m, and the angle between the force and displacement is 60. How much work is done? F Answer: W= F * d * cos W = 20 N * 5 m * cos 60 W = 100 J (.500) = 50.0 J d
Energy and Work • When you lift an object in a gravitational field, work is done on the object. • lifting a box from the floor to the table • When the object falls in a gravitational field, the work is done by the object. • water falling from Niagara Falls to power a generator
Work when moving an object • Lift a 20 kg bag 0.5 m up off the ground. • Carry the 20 kg bag on a level floor for 50 m. • Hold the 20 kg bag still for 2 hours. • Lower the 20 kg bag 0.5 m to the ground. • When did you do work in the procedure above? How much work?
Power • Power is Work per unit time • Power = work done/time interval • Unit: J/s = Watt (W)
Power when moving an object • Lift a 20 kg bag 0.5 m up off the ground in 4.0 s. • Carry a 20 kg bag on a level floor for 50 m in 30 s. • Hold a 20 kg bag still for 2 hours. • Lower a 20 kg bag 0.5 m to the ground in 2.0 s. • What power was used in the above procedure?
Mechanical Energy • Potential Energy • Gravitational Potential Energy • potential energy due to height of an object with mass • gravitational potential energy = m g h • rock above the canyon floor, waterfall, pendulum • Elastic Potential Energy • springs • bow and arrow
Mechanical Energy • Kinetic Energy • kinetic energy due to movement of an object with mass • kinetic energy = ½ m v2 • moving car, rolling ball
Conservation of Energy • Energy is not created or destroyed. It merely changes form. • Forms of energy: Potential, Kinetic, Chemical, Thermal • If friction is neglected, sum of potential and kinetic energies are constant. • Friction generally results in the generation of heat energy • Hard to see heat energy, but it is not lost
Conservation of Energy • assume no friction • Initial KE + PE = final KE + PE • lift a ball above the floor • initial KE = 0 J, initial PE = mgh • drop ball • final KE = ½ mv2, final PE = 0 • Initial = final • mgh = ½ mv2