Calculate the work done by a person weighing 115 lbs, who is carrying goods at a 50-degree angle on their back, exerting a force of 450 N while traveling a distance of 110 feet.

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Answer :

UmyRyan UmyRyan · Answer 1 · 2023-11-27T23:05:56-05:00

The work done by the person is approximately 9704.54 Joules.

To calculate the work done by the person carrying goods, we need to use the formula for work:

[tex]W = Fd \cos \theta[/tex]

Where:

[tex]W[/tex] is the work done.

[tex]F[/tex] is the force exerted.

[tex]d[/tex] is the distance traveled.

[tex]\theta[/tex] is the angle between the force and the direction of movement.

Given data:

Force exerted, [tex]F = 450[/tex] N.
Distance traveled, [tex]d = 110[/tex] feet (converted to meters for consistency in SI units, where 1 foot = 0.3048 meters, [tex]d = 110 \times 0.3048 = 33.528[/tex] meters).
Angle, [tex]\theta = 50^\circ[/tex].

First, we find [tex]\cos 50^\circ[/tex]:

[tex]\cos 50^\circ \approx 0.6428[/tex]

Now, we substitute the values into the formula:

[tex]W = 450 \times 33.528 \times 0.6428[/tex]

[tex]W \approx 450 \times 33.528 \times 0.6428[/tex]

[tex]W \approx 9704.54 \text{ Joules}[/tex]