A sledge loaded with bricks has a total mass of 18.7 kg and is pulled at constan

Question

A sledge loaded with bricks has a total mass of 18.7 kg and is pulled at constant speed by a rope inclined at 19.5° above the horizontal. The sledge moves a distance of 19.4 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500.

A sledge loaded with bricks has a total mass of 18.7 kg and is pulled at constant speed by a rope inclined at 19.5° above the horizontal. The sledge moves a distance of 19.4 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. (a) What is the tension in the rope? 172.925x Your response differs from the correct answer by more than 100%. N (b) How much work is done by the rope on the sledge? 1779 45x (c) What is the mechanical energy lost due to friction?

Explanation / Answer

here,

mass , m = 18.7 kg

theta = 19.5 degree

x = 19.4 m

uk = 0.5

a)

let the tension in the string be T

the normal force , N = ( m * g - T * sin(theta))

as it is moving at constant speed

the net force on object is zero

equating the horiontal forces

T * cos(theta) - uk * N = 0

T * cos(theta) - uk * (m * g - T * sin(theta)) = 0

T * cos(19.5) - 0.5 * ( 18.7 * 9.81 - T * sin(19.5)) = 0

solving for T

T = 82.7 N

the tension in the string is 82.7 N

b)

the work done by the rope on sledge , W1 = T * cos(theta) * x

W1 = 82.7 * cos(19.5) * 19.4 J

W1 = 1512 J = 1.5 KJ

c)

the mechanical energy lost due to friction , E = ff * x

E = uk * ( m * g - T * sin(theta)) * x

E = 0.5 * (18.7 * 9.81 - 82.7 * sin(19.5)) * 19.4 J

E = 1.5 KJ

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