An 18.3 kg block is dragged over a rough, horizontal surface by a constant force of 190 n acting at an angle of angle 31 degrees above the horizontal. the block is displaced 76.5 m and the coefficient of kinetic friction is 0.125.
(a) find the work done by the 190 n force. the acceleration of gravity is
9.8m/s2.
(b) find the magnitude of the work done by the force of friction.

(a)

The displacement occurs in horizontal direction, so to calculate work done, we need to determine the horizontal component of the net force on the block. The external force F acts by pulling (not pushing), this means the angle is 31 above horizontal out (i.e., lifting the block slightly), not in (which would push the block down slightly).

The net force is:

The work done:

The work done on the block is 11682 Joules

(b) Friction acts in the opposite of the line of motion. Its magnitude is determined by the normal force of the surface induced by vertical forces acting on the block - in our case: the gravity and the vertical component of the pulling force. The magnitude of the friction force in terms of the given variables is described in (a) as F_fric:

The friction force does negative work with respect to the work done by the external force:

The magnitude of the work done by friction is the absolute value of the work, i.e., 779 Joules

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