Steps important In the figure below a 3kg block slides along

In the figure below, a 3-kg block slides along a track from one level (points) to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force of 16 N stops the block in a distance d = 0.5m (point B). The height difference h is 1.2 m. Consider a system that consists of the block and Earth. What is the change in gravitational potential energy of the system when the block slides from point A to point B? (36 J) What is the work done by friction when the block slides from point A to point B? (-8 J) Find the block\'s initial kinetic energy (i.e. the kinetic energy at point A). (5/4 N)

Solution

(A) change in gravitational PE = m g (Hf - Hi)

and Hf - Hi = h

change in GPE = m g h = 3 x 10 x 1.2 = 36 J

(B) Work done by friction = f.d = fdcos180

          = - 16 x 0.5 =- 8 J

(C) Work done by all forces = change in KE

work done by friction + work done by gravity = Kf - Ki

{ work done by gravity = - GPE}

- 8 + (-36) = 0 - Ki

Ki = 44 J