Question

A sledge loaded with bricks has a total mass of 18.1 kg and is pulled at constant speed by a rope inclined at 19.5° above the horizontal. The sledge moves a distance of 19.8m 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?
N

(b) How much work is done by the rope on the sledge?
kJ

(c) What is the mechanical energy lost due to friction?
kJ

Answer 1

here,

total mass , m = 18.1 kg

theta = 19.5 dgeree

s = 19.8 m

uk = 0.5

let the tension in the rope be T

equating the forces vertically

N = m * g- T * sin(theta)

equating the forces horizontally

T * cos(theta) = uk * N

T * cos(19.5) = 0.5 * ( 18.1 * 9.81 - T * sin(19.5))

solving for T

T = 80 N

the tension in the string is 80 N

b)

the work is done by the rope on the sledge , W = T * s * cos(theta)

W = 80 * 19.8 * cos(19.5) = 1493.1 J = 1.49 KJ

c)

the mechanical energy lost due to friction , ME = uk * N * s

ME = 0.5 * ( 18.1 * 9.81 - 80 * sin(19.5)) * 19.8 J

ME = 1493 J = 1.49 KJ