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Chapter: 11th Physics : Work, Energy and Power

Solved Example Problems for Conservative and nonconservative forces

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

Solved Example Problems for Conservative and nonconservative forces

Example 4.11

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 dx 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.


Example 4.12

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

= 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 Wk =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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