PlanetPhysics/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.

$$ W = Fd $$

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 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

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