CK-12-Physics - Intermediate

http://www.ck12.org Chapter 16. Electric Potential

FIGURE 16.2

Object is dropped. The change in PE is negative but the work done by

gravity is positive.

If the object has massm, then the change in potential energy when it is lifted is∆PE=mghf−mghi. The change

in potential energy is positive, but the work done by gravity is negative. We can therefore writeW=−∆PE. The

negative sign ensures that the work done by gravity is negative when the object is lifted. The equation is true

regardless of whether the object is lifted or dropped. When the object is dropped, its change in potential energy

is negative and the work done by gravity is positive (the gravitational force and the displacement are in the same

direction when the object falls).

If the object is lifted at a constant velocity, the workWthat an external force does on the object isW=∆PE(no

negative sign). The external force is in the same direction as the displacement of the object when lifting it, and

opposite to the displacement when lowering it.

Check Your Understanding: Review

a. An object of mass 10.0 kg falls from a height of 8.00 m to a height of 3.00 m. What is the change in potential

energy of the object?

Answer:

∆PE=mghf−mghi= ( 10. 0 kg)

(

9. (^81) sm 2

)

( 3. 00 m− 8. 00 m) =− 490. 5 →− 4. 91 × 102 J

b. How much work has the gravitational force done on the object?

Answer:W=−∆PE=−(− 4. 91 × 102 J) = 4. 91 × 102 J

c. Assuming the object was lifted at a constant velocity, how much work would be done on the object by the lifting

force to move it from 3.00 m to 8.00 m?

Answer:W=∆PE→

∆PE=mghf−mghi= ( 10. 0 kg)

(

9. (^81) sm 2

)

( 8. 00 m− 3. 00 m) = 490. 5 → 4. 91 × 102 J

Gravitational Potential

Though gravitational potential is not often discussed in introductory physics books, it may be helpful to define the

concept as a comparison to the electric potential which we will discuss soon.

Let us rewrite the equation expressing the gravitational potential energy(PE=mgh), asPEm =gh. We define the

quantityghas thegravitational potential(the potential energy per unit mass) and represent it with the symbolVg.

Hence,

Vg=gh

Since potential energy and mass are scalar quantities, so is the gravitational potentialVg. Ifgis constant, as it is

near the surface of the Earth, then the gravitational potentialVgis directly proportional to the positionhof the mass.