A sledge loaded with bricks has a total mass of 17.8 kg and is pulled at constan

Question

A sledge loaded with bricks has a total mass of 17.8 kg and is pulled at constant speed by a rope inclined at 20.3 degree above the horizontal. The sledge moves a distance of 19.7 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. What is the tension in the rope? v 67.88 Your response differs from the correct answer by more than 10%. Double check your calculations. N How much work is done by the rope on the sledge? kJ What is the mechanical energy lost due to friction? kJ

Explanation / Answer

let the tension in the rope is T

mass of sledge , m = 17.8 Kg

theta = 20.3 degree

distance , d = 19.7 m

a)

for the sledge to move with constant speed ,

N = mg - T * sin(20.3)

T*cos(20.3) = 0.50 *N

T*cos(20.3) = 0.50 *(17.8 * 9.8 - T * sin(20.3))

solving for T

T = 78.4 N

the tension in the rope is 78.4 N

b)

work done by rope = T * cos(20.3) * d

work done by rope = 19.7 * 78.4 * cos(20.3)

work done by rope = 1448.55 J

the work done by rope is 1448.55 J

c)

as the sledge moves with constant velocity

mechnical energy lost to friction = - 1448.55 J

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