View source for PlanetPhysics/Basic Examples of Calculating Work in Physics

'''Example 1''' . Find in the various units (SI, English and CGS) the [[../Work/|work]] done on a [[../Mass/|mass]] 112 pounds when lifted through 100 feet.

For this example, the equation for work simplifies to just the [[../Thrust/|force]] times the distance that the force is acting.

<math> W = Fd </math>

Plugging in the numbers for SI units

<math>W = \frac{112 [lb]}{1} \cdot \frac{1 [slug]}{32.17 [lb]} \cdot \frac{14.59 [kg]}{1 [slug]} \times  \frac{100 [ft]}{1}
\frac{1 [m]}{3.281[ft]} \cdot 9.806 [m/s^2] = 15,180 [joules]</math>

Plugging in the numbers for English units

<math> W = 112 [lb] \times 100 [ft] = 11,200 [ft-lb]</math>

Plugging in the numbers for CGS units

<math> W = \frac{112 [lb]}{1} \cdot \frac{ 453.6 [gram]}{1 [lb]} \times \frac{100 [ft]}{1} \cdot \frac{ 1 [m]}{ 3.281 [ft]} \cdot \frac{100 [cm]}{ 1 [m]} \cdot \frac{9.806 [m/s^2]}{1} \cdot \frac{100 [cm]}{1 [m]} = 1.518 \times 10^{11} [ergs] </math>

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

The force for this example is a [[../Bijective/|function]] of <math>x</math>

<math> F(x) = 5x </math>

integrating from [[../Position/|position]] 1 to 2 yields the work

<math> W = \int_1^{10} 5x dx = \bigg |_1^{10} \frac{5}{2} x^2 = 250 - 2.5 [N \cdot m] = 247.5 [N \cdot m] </math>

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