basic examples of calculating work in physics

Example 1. Find in the various units (SI, English and CGS) the work done on a mass 112 pounds when lifted through 100 feet.

For this example, the equation for work simplifies to just the force times the distance that the force is acting.

W = F d

Plugging in the numbers for SI units

W = 112-[lb]⋅ 1[slug]-⋅ 14.59[kg-]× 100[ft]--1[m-]--⋅ 9.806[m ∕s2] = 15,180[joules] 1 32.17 [lb] 1[slug ] 1 3.281[ft]

Plugging in the numbers for English units

W = 112[lb] × 100[ft] = 11,200[ft − lb]

Plugging in the numbers for CGS units

112[lb] 453.6[gram ] 100[ft] 1[m] 100 [cm ] 9.806[m ∕s2]100 [cm ] W = ------⋅------------× -------⋅--------⋅--------⋅-----------⋅-------- = 1.518×1011 [ergs] 1 1[lb] 1 3.281 [f t] 1[m ] 1 1[m ]

Example 2. How much mork is done by a force of 5x newtons acting in the x-direction upon a particle while it is displaced from x = 1[m] to x = 10[m]?

The force for this example is a function of x

F(x) = 5x

integrating from position 1 to 2 yields the work

∫ 10 105- 2 W = 5xdx = |1 2x = 250 − 2.5 [N ⋅ m ] = 247.5 [N ⋅ m ] 1

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