Problem :
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total work done on the block over the same distance?
Unused fields are stripped. PENs are stored in a hash table loaded at run-time. User 'enterprises' file is loaded from the personal config dir. Misc make-sminmpec.pl improvements and fixes. Note: names of type 'Entity (formerly.)' have the formerly part commented out for a cleaner output. Choose the direction of the positive y -axis. It’s easiest to make the same choice we used for freely falling objects in Section 2.5. You can divide Green Lantern’s fall into two parts: from the top of the building to the halfway point and from the halfway point to the ground. You know that the second part of the fall lasts 1.00 s.
Finding the work done by the 50 N force is quite simple. Since it is applied parallel to the incline, the work done is simply W = Fx = (50)(10) = 500 J.
Finding the total work done on the block is more complex. The first step is to find the net force acting upon the block. To do so we draw a free body diagram:Because of its weight, mg, the block experiences a force down the incline of magnitude mg sin 30 = (5)(9.8)(.5) = 24.5 N. In addition, a frictional force is felt opposing the motion, and thus down the incline. Its magnitude is given by Fk = μFN = (.25)(mg cos 30) = 10.6 N. In addition, the normal force and the component of the gravitational force that is perpendicular to the incline cancel exactly. Thus the net force acting on the block is: 50 N -24.5 N -10.6 N = 14.9 N, directed up the incline. It is this net force that exerts a ìnet workî on the block. Thus the work done on the block is W = Fx = (14.9)(10) = 149 J.