A sledge loaded with bricks has a total mass of 19.0 kg and is pulled at constan
ID: 1538891 • Letter: A
Question
A sledge loaded with bricks has a total mass of 19.0 kg and is pulled at constant speed by a rope inclined at 21.0° above the horizontal. The sledge moves a distance of 20.2 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?
Your response differs from the correct answer by more than 10%. Double check your calculations. N
(b) How much work is done by the rope on the sledge?
Your response differs from the correct answer by more than 10%. Double check your calculations. kJ
(c) What is the mechanical energy lost due to friction?
Explanation / Answer
a)
let T is the tension in the string.
As the sledge is moving with constant speed, net force acting on it must be zero.
let N is the normal force on the sledge.
apply, Fnety = 0
N + T*sin(21) - m*g = 0
N = m*g - T*sin(21)
Apply, Fnetx = 0
T*cos(21) - fk = 0
T*cos*(21) - mue_k*N = 0
T*cos(21) - mue_k*(m*g - T*sin(21)) = 0
T*(cos(21) + mue_k*sin(21)) = mue_k*m*g
T = mue_k*m*g/(cos(21) + mue_k*sin(21))
= 0.5*19*9.8/(cos(21) + 0.5*sin(21))
= 83.7 N
b) Workdone by the rope, W_rope = T*d*cos(21)
= 83.7*20.2*cos(21)
= 1.58*10^3 J
= 1.58 kJ
c) mechaincal energy lost = -Workdone by friction
= 1.58*10^3 J or 1.58 kJ