when can i use sin or cos in the work=force x distance x sin/cos(B)??

Question

in the equation work = Fdcos/sin(B), when will i use the sine and the cosine? what tpye of situations???

Answer 1

to simplify this, cos(B)/sin(B) is really just Cot(B)
the cotangent is the adjacent side over the opposite side, like
if you have a triangle like this:


w
ww 5 The left side is length 4 (a 3,4,5, right triangle)
www
wwww
wwwwww
3
take for example the bottom-right angle. (I'll call that angle B) cot(B) is the ratio of the side length 3/4 So, 3/4=Cot(B)

say for example you need to figure out the amount of work it took to push a box up that slope on the triangle. you have the amount of (constant) force it took, and you have the distances of the non-hypoteneuse sides. (3 and 4) (the other side is 5, obviously)
to solve for the work done do this:
take the total distance pushed, multiply that by the force amount, and multiply that by cot (3/4)
let's say that you pushed the box with 20 newtons of force, up the 4 meter ramp.
so, W=(20N)(5m)(cot (3/4))= 413.173 J
J=joules, which is the unit of work.
Note: If you do not have a "Cot " button on your calculator, you can use Tan and flip the fraction from 3/4 to 4/3
Tan is the opposite of cot, all you gotta do is flip that fraction!


It has nothing to do with gravity, you already overcame gravity when you pushed with 20 Newtons of force

Answer 2

You use w = f * d when the force is in the same direction as the displacement and the force is constant.

You use w = f * d * cos(theta) where theta is the angle between the force and displacement. Use this when the force is constant but in a different direction from the displacement.

Technically speaking. The formula is w = f ∙ d.
where these are all vectors and dot means to take the dot product.

Answer 3

force is a vector,,, has a component on the X axis and a component on the Y axis, so the X axis component would be Fcosof the angle, and the vertical component would be Fsen of the angle