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.

$\displaystyle W = Fd $

Plugging in the numbers for SI units

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

Plugging in the numbers for English units

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

Plugging in the numbers for CGS units

$\displaystyle W = \frac{112 [lb]}{1} \cdot \frac{ 453.6 [gram]}{1 [lb]} \times ...
...c{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 while it is displaced from $ x = 1 [m]$ to $ x = 10 [m]$ ?

The force for this example is a function of $ x$

$\displaystyle F(x) = 5x $

integrating from position 1 to 2 yields the work

$\displaystyle W = \int_1^{10} 5x dx = \bigg \vert _1^{10} \frac{5}{2} x^2 = 250 - 2.5 [N \cdot m] = 247.5 [N \cdot m] $



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