A rope is thrown over a beam, and one end is tied to a 300 N bundle of lumber. You pull the free end of the rope 2 m with a force of 400 N to lift the lumber off the ground. How much work have you...

A rope is thrown over a beam, and one end is tied to a 300 N bundle of lumber. You pull the free end of the rope 2 m with a force of 400 N to lift the lumber off the ground. How much work have you done?

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electreto05 | College Teacher | (Level 1) Assistant Educator

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The work done by a force (F) to move a body a distance (d) can be calculated by the following equation:

W = F*d*cos θ

Where:

F,  is the resulting force applied to the body.

d,  is the distance traveled by the body

θ,  is the angle between the direction of force and the direction of motion.

When the force is applied in the same direction of motion, we have:

W = F*d

In our case we must find the resulting force applied in the vertical direction. Let's keep in mind that, at the ends of the rope, acts a tension (T). Under these conditions, the resultant force of the system is:

Fy = - (w) + T - T + F

Fy = - (300) + (400) = 100 N

W = Fy*d = (100)(2) = 200 J

The work that has been done is 200 J

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