Force Moving an Object Over a Distance

Using physics, y’all can calculate the work required to motion an object over a given altitude. Motion is needed for work to be done. For piece of work to exist done, a net force has to move an object through a displacement. Work is a product of strength and displacement.

Hither’due south an instance: Say that you’re pushing a huge gold ingot habitation, equally this effigy shows. How much work practise you have to do to go it home? To observe work, you need to know both strength and displacement. First, find out how much force pushing the ingot requires.

Suppose that the kinetic coefficient of friction,

between the ingot and the ground is 0.250 and that the ingot has a mass of ane,000 kilograms. What’s the forcefulness yous have to exert to go on the ingot moving without accelerating it? Kickoff with this equation for the strength of friction:

Bold that the route is flat, the magnitude of the normal strength,
F

_North

,
is merely
mg
(mass times the dispatch due to gravity). That means that

where
m
is the mass of the ingot and
g
is the acceleration due to gravity on the surface of the World. Plugging in the numbers gives y’all the following:

You have to employ a force equal in magnitude to the force of friction (that is, 2,450 newtons) to go along the ingot moving without accelerating.

Y’all know the forcefulness, and then to notice work, yous need to know the displacement. Say that your house is 3 kilometers, or 3,000 meters, abroad. To get the ingot home, you accept to do this much work:

Because you lot’re pushing the ingot with a force that’due south parallel to the footing, the bending between
F
and
s
is 0 degrees, and cos 0 degrees = 1, so plugging in the numbers gives you the following:

You need to do seven.35 × 10⁶
joules of work to motion your ingot home. Want some perspective? Well, to lift i kilogram i meter straight up, you have to supply a strength of 9.8 newtons (about two.2 pounds) over that distance, which takes 9.viii joules of work. To go your ingot habitation, you need 750,000 times that. Put another fashion, 1 kilocalorie equals 4,186 joules. A kilocalorie is commonly called a Calorie (capital C) in nutrition; therefore, to motion the ingot home, you need to expend about one,755 Calories. Time to get out the energy bars!