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Physics · Ch 4 — Work, Energy and Power

Potential energy near the surface of the Earth

4.2.5

Potential energy near the surface of the Earth

Near the Earth's surface, gravity is essentially a constant force, F⃗g=−mg j^\vec F_g = -mg\,\hat j (taking "up" as positive). To lift a body of mass mm through a height hh at constant velocity, an external force F⃗a\vec F_a equal in magnitude but opposite in direction to gravity must be applied, F⃗a=+mg j^\vec F_a = +mg\,\hat j; since the applied force and the (upward) displacement are in the same direction, θ=0\theta = 0 and cos⁡θ=1\cos\theta = 1 throughout.

Using the general definition of potential energy from the previous section,

U=∫0hF⃗a⋅dr⃗=∫0h(mg)(dr)=mg hU = \int_0^h \vec F_a\cdot d\vec r = \int_0^h (mg)(dr) = mg\,h

U=mgh\boxed{U = mgh} …

Figure 4.8Gravitational potential energy

What this figure shows. A body of mass m is shown being raised vertically through a height h above a chosen reference level, moved by an external applied force that is equal in magnitude and opposite in direction to the downward gravitational force mg acting on the body. Because the applied force and the displacement both point upward and the motion is at constant velocity, all of the external agency's work is stored in the body as gravitational potential energy U = mgh, which is released as kinetic e …

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