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.

$W=Fd$

Plugging in the numbers for SI units

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

Plugging in the numbers for English units

$W=112[lb]\times 100[ft]=11,200[ft-lb]$

Plugging in the numbers for CGS units

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

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

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

$F(x)=5x$

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

$W=\underset{1}{\overset{10}{\int }}5xdx={|}_1^{10}\frac{5}{2}{x}^2=250-2.5[N\cdot m]=247.5[N\cdot m]$