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A person lifts a 4.5 kg cement block a vertical distance of 1.2 m and then Carrie’s the block horizontally 7.3 m. Determine the work done by the person and by the force of gravity.

User Brian Hogan
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1 Answer

15 votes
15 votes

Answer:

+52.97 J for the person, -52.97 J for the force of gravity

Step-by-step explanation:

We have two phases: 1) vertical lift and 2) horizontal carrying.

In general, the work is given by force * distance if force and path are parallel. It is 0 if force and path are perpendicular. More complex form if force and path form an angle or if the force isn't constant.

The person is lifting an object, therefore at minimum we need to win gravity.

The force of gravity is, by definition, mass * gravity.

In this case, it's Fg = m * g = 4.5 kg * 9.81 m/s^2 = 44.14 N

This is the minimum force to lift that object. The problem isn't talking about surpassing this force, therefore we assume the person is lifting the object using exactly 44.14 N.

In the first phase, the force of gravity and the path are parallel, therefore the work is given by: force * distance:

W = Fg * d = 44.14 N * 1.2 m = 52.97 J

In the second phase, the person only needs to carry the block, therefore the force is the same as before, but, the force and the path aren't parallel: they're perpendicular. In this case, the work is 0 J.

Finally, the total work done by the person is: 52.97 J + 0 J = 52.97 J

About the force of gravity, It always has the same direction and intensity of the force of the person, therefore all previous observation and computations are valid exactly as they are, and the work done by the force of gravity is the same of that found just now: 52.97 J

If you also need signs (positive or negative work), about the person, his force and the path are of same sign, therefore his work is positive (+52.97 J). The force of gravity is of opposite sign, therefore its work is -52.97 J

User Emanuel Trandafir
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