Solved Example Problems for Conservative and nonconservative forces
Compute the work done by the gravitational force for the following cases
(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.
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)
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 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.