A man pulls a 10-kg box across a smooth floor with a force of 71 newtons at an angle of 23 degrees and for a distance of 97 meters. How much work, to the nearest joule, does he do?
What is the component of horizontal force? ANS: 71*cos23
work = horizontal force * distance
To determine the work done, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Force is the magnitude of the force applied (in newtons),
- Distance is the distance covered (in meters), and
- θ is the angle between the force and the direction of motion (in degrees).
Given:
- The force applied is 71 newtons,
- The distance covered is 97 meters, and
- The angle between the force and the direction of motion is 23 degrees.
Substituting these values into the formula, we have:
Work = 71 newtons × 97 meters × cos(23 degrees)
Now, let's calculate the cos(23 degrees) first:
cos(23 degrees) ≈ 0.9205
Plugging this value back into the formula, we find:
Work ≈ 71 newtons × 97 meters × 0.9205
Work ≈ 6588.425 joules
Therefore, the man does approximately 6588.425 joules of work.