A 100 N force directed at 60 above the horizontal pulls a box 2 m horizontally across a floor. How much work was done? A. 50 J
B. 20 J
C. 100 J
D. 200 J

C. 100 J

Explanation:

If the 60 you wrote is the degree (60°)

Work done = forcexcos x distance

W= 100x cos 60 x2

W= 100 J

100 J

Explanation:

Work done is the product of force and distance. The distance here is easy; it's just 2 m because it was pulled horizontally. The force, on the other hand, requires some more work, no puns intended!

We know the applied force is at an angle. Since work is parallel to the distance, the force used to calculate work must be parallel to the distance as well. This means we must use the horizontal component of the force. This, consequently, calls for the horizontal component of the angle.

Here, that horizontal component is the cosine of theta, cos θ, because the horizontal component must be adjacent to the angle. We know the angle in this case; θ is 60°. So, to find the component of the force parallel to the floor, we must multiply the total force by cos θ.

Here, θ = 60°, and the total force is 100 N. Therefore, the horizontal force equals 100 N × cos 60°. As for cos 60°, its value is 0.5. This means the horizontal force equals 100 N × cos 60° = 50 N.

From here, the work is that force, those 50 N, times the distance the box was pulled, 2 m. Therefore, work equals 50 N × 2 m = 50 N × m = 50 J.

In summary, the total work done is 50 J.

I hope you understand my explanation! Please have a great day!

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