Energy, Work, and Simple Machines Chapter 10 Energy, Work, and Simple Machines
10.1 Energy and Work Energy is the ability to produce change in itself or the environment. Energy of Motion: vf2 = vi2 + 2ad Rearranging vf2 - vi2 = 2ad Substituting Newton’s second law vf2 - vi2 = 2Fd/m
Multiply both sides by ½ m ½ mvf2 – ½ mvi2 = Fd Kinetic energy KE = ½ mv2 Work-Energy Theorem ΔKE = W When work is done on an object, a change in kinetic energy results.
Work: Through the process of doing work, energy can transfer from the environment to the object and back again! The equation for work is W = Fd For constant forces in the direction of the motion. Unit of work is the joule (J)
Constant force at an angle: Work (angle between force and displacement). W = Fd cos
Power is measured in watts (joule/second) The rate at which work is done P = W/t Power is measured in watts (joule/second)
PSS Sketch the problem. Establish a coordinate system Draw a vector diagram. List known and unknowns. Use the basic equation for work when a constant force is exerted in the same direction as the displacement. Or the equation W = Fd cos which will work in all situations.
Use the work-energy theorem to determine the change in energy of the system. Use work and time to find power. Check your answer.
10.2 Machines Simple and Compound Machines Mechanical Advantage The output work can never be greater than the input work The machine simply aids in the transfer of energy. Mechanical Advantage The force you exert on a machine is called the effort force Fe The force exerted by the machine is called the resistance force Fr
This equation can be rewritten using the definition of work The ratio of resistance force to effort force, is called the mechanical advantage. Mechanical Advantage MA = Fr / Fe This equation can be rewritten using the definition of work Wo = Wi or Frdr = Fede Rearranging this gives Fr/Fe = de/dr
We know that the mechanical advantage is given by MA = Fr/Fe For an ideal machine, MA = de/dr Because this equation is characteristic of an ideal machine, the mechanical advantage is called the Ideal Mechanical Advantage IMA = de/dr
Efficiency: The efficiency of a machine is defined as the ratio of output work to input work. Efficiency (%) = Wo/Wi X 100 An ideal machine has equal output and input work and the efficiency is 100%. In terms of mechanical advantage and ideal machine advantage Efficiency (%) = (Fr/Fe)/(de/dr) X 100 Efficiency (%) = MA / IMA X 100
Simple machines: Most simple machines are combinations of one or more of the six simple machines. They are the lever, pulley, wheel and axel, inclined plane, wedge, and screw. The IMA of all machines is the ratio of distances moved.
Compound machines: A compound machine consists of two or more simple machines linked so that the resistance force of one machine becomes the effort force of the second. The mechanical advantage of a compound machine is the product of the mechanical advantage of the simple machines it is made up of. MA = MA machine 1 X MA machine 2