10/3 Work Power and Energy Work=force X distance Units-force= mass X acceleration (kg m/s2) (kg m/s2)m?kg m2/s2?Nm?(j)oules Energy is the ability to do work Energy and work have the same units ? j Power= work/time or energy/time [units ? kg m2/s3?Nm/s?j/s?(w)atts] Work, energy and power are scalars The work done always results in an equal change in energy ?W = ?E Mechanical energy Potential energy- the energy of position Potential energy results from mass bring positioned so that it can do work. This PE is equal to the work done to get the mass into position. The PE of the mass at a height is PE=mgh Kinetic energy- the energy of moving mass Example A 1 kg steel ball atop a 1 m desk has PE = mgh = 1 kg X10 m/s2 X 1 m = 10 j with respectt to the floor. But if the floor is higher than the ground outside, the PE with respect to it will be larger than the PE with respect to the floor and when lying on the floor, the ball still has PE w/r/t the ground outside the room. Gravitational PE will mostly be discussed although PE can come from stretched or compressed springs or elastic straps, chemical processes, or electromagnetic effects, etc. Work and Energy Energy can not be created or destroyed, simple rearranged. Example: A mass at height h has PE = mgh. If the mass is allowed to fall, its PE decreases in direct proportion to the decrease in h (e.g. at h/2, PE is 1/2h). Since energy cannot be destroyed, this energy must transform into another form. The other form is kinetic energy the energy of motion. As the mass falls, PE is converted to KE = 1/2mv2 so that KE is maximum/minimum when PE is minimum/maximum. Calculate the speed of a 10 kg steel ball at the bottom of a 10 m fall from rest using: A) the method from chapter 3: V(d) = a?t = a(2d/a)1/2 =10m/s2(2 X 10 m/10 m/s2)1/2 V(10 m) = 10 X ?2 m/s =14.14 m/s B) by energy conservation mgh = 1/2mv2 or v = ?(2gh)= ?(2X10m/s210m) = 14.14 m/s Power=the rate at which work is done More power is required to do a given amount of work in a short time than to do the same work in a long time. Example using horsepower: 1 hp = 550 lb ft/s
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