This is great!I’m getting paid for doing no work!
CAN YOU DO NEGATIVE WORKING? Force and distance in same direction = + work Force and distance in opposite directions = - work
W = Fd(cos ө)…so when the applied force isperpendicular to the distance,you end up with zero work!
CALCULATION OF WORK Just as velocities may be integrated over time to obtain atotal distance, by the fundamental theorem of calculus,the total work along a path is similarly the time-integralof instantaneous power applied along the trajectory of thepoint of application.Work is the result of a force on a point that movesthrough a distance. As the point moves it follows a curveX with a velocity v at each instant. The small amount ofwork δW that occurs over an instant of time δt is given by
where the F.v is the power overthe instant δt. The sum of thesesmall amounts of work over thetrajectory of the point yields thework.
WORK DONE BY A SPRINGA horizontal spring exerts a force F=(kx, 0, 0) that is proportional to itsdeflection in the x direction. The work of this spring on a body movingalong the space curve X(t) = (x(t), y(t), z(t)), is calculated using its velocity,V=(vx, vy, vz), to obtainFor convenience, consider contact with the spring occurs at t=0, then theintegral of the product of the distance x and the x-velocity, xvx, is (1/2)x2.
WORK DONE BY A GRAVITYGravity exerts a constant downward force F=(0, 0, W) on the center of mass ofa body moving near the surface of the earth. The work of gravity on a bodymoving along a trajectory X(t) = (x(t), y(t), z(t)), such as the track of a rollercoaster is calculated using its velocity, V=(vx, vy, vz), to obtain. where the integral of the vertical component of velocity is the vertical distance. Notice that the work of gravity depends only on the vertical movement of the curve X(t).
THE WORK-ENERGY THEOREMWhen a net external force does work W onan object, the kinetic energy of the objectchanges from its initial value of KE0 to a finalvalue of KEf, the difference between the twovalues being equal to the work: 1 2 1 2 W KE f KE0 mv f mv0 2 2 20
The work done in liftingthe mass gave the massgravitational potentialenergy.Potential energy thenbecomes kinetic energy.Kinetic energy then doeswork to push stake intoground.
Mechanical energy is the energy which ispossessed by an object due to its motionor its stored energy of position.Mechanical energy can be either kineticenergy or potential energy.
The 1st Law of Thermodynamics and the Lawof Conservation of Energy state that thealgebraic sum of these energy changes andtransfers must add up to zero, accountingfor all changes relative to the system. W Q E W + Q = ∆E
So for mechanics neglecting Q W = ∆Ek + ∆Eg + ∆Eel+ ∆Echem+∆Eint
All Energy Potential Kinetic Energy EnergyGravitation Elastic Chemical Potential Potential Potential Energy Energy Energy
o Energy that is stored and waiting to be used later
o Energy an object has due to its motiono K.E. = .5(mass x speed2)
Energy Storage Mode Equations: 1) EK = ½mv2 2) Eg = mgh 3) Eel = ½kx2