Physics : Work, Energy and Power : Conservative and nonconservative forces

Solved Example Problems for Conservative and nonconservative forces

Compute the work done by the gravitational force for the following cases

*Solution*

(As the displacement is in two dimension; unit vectors and are used)

a. Since the motion is only vertical, horizontal displacement component d*x* is zero. Hence, work done by the force along path 1 (of distance h).

Therefore, the total work done by the force along the path 2 is

Note that the work done by the conservative force is independent of the path.

Consider an object of mass 2 kg moved by an external force 20 N in a surface having coefficient of kinetic friction 0.9 to a distance 10 m. What is the work done by the external force and kinetic friction ? Comment on the result. (Assume g = 10 ms-2)

*Solution*

*m *= 2 kg,* d *= 10 m,* Fext *= 20 N,* **k** *= 0.9.* *When an object is in motion on the horizontal surface, it experiences two forces.

a. External force, *Fext* = 20 N

b. Kinetic friction,

*fk =μkmg *= 0.9x(2)x10=18N.

The work done by the external force Wext = Fs = 20x20 =200J

The work done by the force of kinetic friction W*k* =*fkd* = (-18) x10=-180J Here the negative sign implies that the force of kinetic friction is pposite to the direction of displacement.

The total work done on the object

Wtotal = Wext + Wk = 200 J – 180 J = 20 J .

Since the friction is a non-conservative force, out of 200 J given by the external force, the 180 J is lost and it can not be recovered.

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11th Physics : Work, Energy and Power : Solved Example Problems for Conservative and nonconservative forces |

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