Starting from rest, a 4.6-kg blockslides 2.60 m down a rough 30.0°incline. The c

Question

Starting from rest, a 4.6-kg blockslides 2.60 m down a rough 30.0°incline. The coefficient of kinetic friction between the block andthe incline is µk = 0.436. (a) Determine the work done by the force ofgravity.
1 J

(b) Determine the work done by the friction force between block andincline.
2 J

(c) Determine the work done by the normal force.
3 J

(d) Qualitatively, how would the answers change if a shorter rampat steeper angle were used to span the same vertical height?
4 (a) Determine the work done by the force ofgravity.
1 J

(b) Determine the work done by the friction force between block andincline.
2 J

(c) Determine the work done by the normal force.
3 J

(d) Qualitatively, how would the answers change if a shorter rampat steeper angle were used to span the same vertical height?
4

Explanation / Answer

(a) The workdone by gravity is                 W = Fd sin                     = mgdsin                     = (4.6kg)(9.80m/s²)(2.60m)sin30.0°                     = 58.604J (b) Workdone by frictional force               W = -mgdcos                    = -(0.436)(4.60kg)(9.80m/s²)(2.60m)cos30.0°                    = -44.25J (c) Since the normal force is perpendicular to the direction of theblock’s motion, it does zero work. (d) Since friction is non conservative, the work done by frictionwill be reduced since it depends on the normal force mgcos which will be less as a result of the steeperangle.

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