A sledge loaded with bricks has a total mass of 17.4 kg and is pulled at constan

Question

A sledge loaded with bricks has a total mass of 17.4 kg and is pulled at constant speed by a ropeinclined at 20.2° above the horizontal. The sledge moves adistance of 19.3 m on a horizontalsurface. The coefficient of kinetic friction between the sledge andsurface is 0.500. (a) What is the tension in the rope?
1 N

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

(c) What is the mechanical energy lost due to friction?
3 kJ (a) What is the tension in the rope?
1 N

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

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

Explanation / Answer

a) The horizontal component      T cos - Fk = ma = m(0) ==> T cos = Fk             = kN             = k * (mg - Tsin)      T = k*mg /(cos + ksin)         = 0.5*17.4*9.8 /(cos20.2 + 0.5*sin20.2 )         = 66.41 N b) Workdone by the rope on the sledge is       W = T* S =66.41 * 19.3 = 1.281kJ c) The mechanical energy lost due to friction       W = Fk*S =k * (mg - Tsin) *S = 0.5 * (17.4*9.8 - 66.41*sin20.2) =0.0739kJ

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