You are helping to build a barn and will need to pull some boards up a hill to t

Question

You are helping to build a barn and will need to pull some boards up a hill to the building site using a rope attached to a winch. In order to buy the rope, you need to know how strong the rope must be and decide to do a quick calculation for this. The stacks of boards weigh 200 lbs. at most and the hill is at an angle of 35° from the horizontal. You estimate that the coefficient of kinetic friction between the boards and the hill is 0.90. When pulling stacks up the hill, you will make sure that the rope stays parallel to the surface of the hill and the acceleration of the boards is never more than 0.80 m/s Your answer must be organized, clear, and include the elements of the problem solving p 1. Focus the Problem (10 pts.) 2. Describe the Physies (10 pts.) 2. Describe the Physics (10 pts.) 3. Plan the Solution (25 pts.) 4. Execute and Evaluate (5 pts.)

Explanation / Answer

given weight W = m*g = 200lbs = 2000*4.448 = 8896 N

mass = m = W/g = 907.75 kg

Fg along the plane = Fg = m*g*sin35 acts down the plane

normal force Fn = m*g*cos35

frictional force fk = uk*m*g*cos35 acts down the plane

tension in the strin acts up the plane

acceleration a = 0.8 m/s^2

Fnet = T - Fg - fk

but Fnet = m*a

T = Fg + fk + m*a

T = (8896*sin35)+(0.9*8896*cos35)+(907.75*0.8) = 12387.19 N <-------answer

the rope should withstand a tension T

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