Answer to Question #267255 in Mechanics | Relativity for Victoria Rodriguez

Question

A 19.8 kg block is dragged over a rough, hor izontal surface by a constant force of 174 N acting at an angle of 25.8° above the horizon tal . The block is displaced 63.9 m, and the coefficient of kinetic friction is 0.123 .

Answer 1

A 19.8 kg block is dragged over a rough, hor izontal surface by a constant force of 174 N acting at an angle of 25.8° above the horizon tal . The block is displaced 63.9 m, and the coefficient of kinetic friction is 0.123 .

a. Find the work done by the 174 N force. The acceleration of gravity is 9.8 m/s^2

b. Find the magnitude of the work done by the force of friction.

a.

$Work = Force \times Distance \times cos θ \\ Work = 174 \times 63.9 \times cos(25.8°) \\ Work = 10010.28 \;J$

b.

$N+F_y = P \\ N = P-F_y \\ N = m \times g -174 \times sin θ \\ N = 19.8 \times 9.8 -174 \times sin(25.8°) \\ N = 11897.88309 \;Newtons \\ F_a = N \times \mu \\ F_a = 118.309 \times 0.123 = 14.552 \; Newtons \\ Work = 14.552 \times 63.9 = 929.873 \;J$