4/10 Opener

Work, Power, & Energy

Work Work is done when a force acts upon an object causing a displacement w=f x d x cos Remember displacement is the overall change in position (vector quantity) Theta is defined as the angle between the force and the displacement  Vertical forces (theta = 90) cannot do work on horizontally displaced objects because cos(90)=0, therefore w=0 Negative work refers to forces that counteract displacement by another force IE an applied force moves an object rightward horizontally and a frictional force slows the object in the leftward direction. (theta = 180) Units of work are Joules (j) or Newton Meters (Nm)

Practice Problems  Determine whether these statements represent examples of work.  1.  No, no displacement 2. Yes, Force=Grav, Displacement=down 3. No, the force doesn't cause the displacement  4. Yes, Force=propellant, causes displacement  #3 It was mentioned earlier that the waiter does not do work upon the tray as he carries it across the room. The force supplied by the waiter on the tray is an upward force and the displacement of the tray is a horizontal displacement. As such, the angle between the force and the displacement is 90 degrees. If the work done by the waiter on the tray were to be calculated, then the results would be 0. Regardless of the magnitude of the force and displacement, F*d*cosine 90 degrees is 0 (since the cosine of 90 degrees is 0). A vertical force can never cause a horizontal displacement; thus, a vertical force does not do work on a horizontally displaced object!!

Practice Problems  A.500 J B.433 J C. 735 J

Potential Energy The stored energy of position possessed by an object Gravitiational potential energy (Pegrav) The energy stored in an object as the result of its vertical position or height (based on the gravitational attraction of the earth for the object) Based on mass and object height (usually from the earth’s surface) Mass and Height are directly related to Pegrav Pegrav=mass x g x height Units=Joules Elastic potential energy The energy stored in elastic materials based on their ability to stretch and compress PEspring= .5 x K x X2 K= spring constant (Depends on spring properties such as stiffness) X= the distance the spring is stretched from it’s equilibrium position Equilibrium position the natural position of the spring when no forces are being applied Greater stretch ability = more stored energy Spring constant is the slope of the graph X vs Force

Practice Question  A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat- top? 13.2J

Kinetic Energy The energy of an object in motion Vibrational Kinetic Energy Motions that repeat in a cycle Rotational Kinetic Energy KErot=.5Iw2 Translational Kinetic Energy KE=.5mv2 Units=Joules=kg(m/s)2 Rotational I=Inertia w=angular velocity How are mass and velocity related in this equation?

Practice Questions  Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s. 1.05 x 10^5 J

Mechanical Energy An object that possesses Mechanical Energy has the ability to do work Total Mechanical Energy (TME): Sum of the potential and kinetic energy TME=PEgrav + PEspring + KE

Power The rate at which work is done Power = work/time therefore power= (F x d x cos)/t UNITS= watt OR joule/second 1 horsepower = 750 watts A more powerful engine can do the same amount of work in less time How are variables related in this equation?

Practice Problem  A tired squirrel (mass of approximately 1 kg) does push-ups by applying a force to elevate its center-of-mass by 5 cm in order to do a mere 0.50 Joule of work. If the tired squirrel does all this work in 2 seconds, then determine its power. .5J/2s=.25W

1/22 Finish up Stopping Distance Lab To Setup sensors go to experiment setup sensors Show all Select the photogate and change to “Gate Timing” then input length of object (your car) Remember 1m=100cm 