A sledge loaded with bricks has a total mass of 18.1 kg and is pulled at constan
ID: 1681833 • Letter: A
Question
A sledge loaded with bricks has a total mass of 18.1 kg and is pulled at constant speed by a ropeinclined at 19.4° 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
The equation of motion along the horizontal direction is T cos - fk = 0 ==> T cos = fk = k N.........1 Along the vertical direction N + T sin - mg = 0 ==> N = mg - T sin .........2 From eq 1 and 2 we have Tcos = k mg - k Tsin ==> T = k mg / (cos + k sin) = 0.5 * 18.1 * 9.8 / (cos19.4 + 0.5 sin19.4 ) = 79.95 N (b) Wordone by rope W = Td cos = 79.95 * 19.3 * cos19.4 = 1455.22 J = 1.455 kJ (c) The mechanical energy lost due to friction = W =1455.22 J = 1.455 kJ
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