Work+&+KE

=**__Work & Kinetic Energy__**=

**Work**
In physics //work// is the product of a force and the resulting displacement. Work only occurs when there is motion and the force is parallel to movement. For example, when an object is lifted work is done. However, when an object is simply suspended in the air, regardless of the difficulty involved in keeping the object off the ground. When one moves while holding the object, work is done in the direction of movement. There is no work involved with centripetal either.



Equations of Work
W = F · d

which becomes

W = Fd cosθ

W = Work F = Force d = Distance

Work is measured in Joules (J), which are equivalent to Newton-meters (N-m), which are equivalent to kilogram-meters squared per second squared (kg-m²/s² ).

1 calorie (cal) = 4.2 J

Work-Energy Theorem
When work is done to accelerate a body, energy is conserved.

W = Fd

W = (ma)d

W = m [(v^2 - vo^2)/2]

W= (mv^2)/2 - (mvo^2)/2

W = k - ko

W = ΔK

Work done by a spring force
F = -kx

Plug into work equation.

Work done by a general variable force
Calculate this from the area underneath a graph where possible.

Alternatively, the definite integral of force can be taken. In equation form, it is: Integral from xo to x of F dx

That becomes: the Integral from xo to x of -kx dx

That becomes: W = [(-kx^2)/2] plug in x and xo

That becomes: W = (-kx^2)/2 + (kxo^2)/2

That becomes: W = (1/2)k (xo^2 - x^2)

An alternate representation is W = Fx cosθ

Power
Power is the rate of work, and is measured in Watts (W) which is a Joule/second.

P = W/t

P = (Fd)/t = Fv

Sometimes, it is measures in horsepower.

1hp = 746 W

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