Applications of Dot Product: Finding Force Components on an Inclined Plane

[Macleef]

Homework Statement

15) In Question 14, if the ramp makes an angle of 20 degrees with the level ground. Find the magnitude of the force tending to lift the crate vertically.

Textbook Answer for Question 15: 108.3 N

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14) A crate is being dragged up a ramp by a 125 N force applies at an angle of 40 degrees to the ramp. Find the magnitude of the force in the direction of motion (Answer is 95.8 N).

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Homework Equations

u (dot) v = |u||v|cosx

The Attempt at a Solution

I have half of the diagram because I don't understand the rest of the problem:

 

[rootX]

draw a box on the ramp;
in FBD= W points down and your points up in +ve y ...
and box is stationary so Fnet = 0

 

[Macleef]

What? I don't understand what you meant by "in FBD= W points down and your points up in +ve y"

 

[rootX]

i meant your force, that is asked, and W is the weight of the box
ops, sorry I missed force ><

and then this leaves you with a simply geometric problem where you find the thetas, and something simple like Fx = F.cos theta and Fy = F.sin theta
(it isn't much of dot product problem, but just dividing the F into x and y components )

This is a very common example and you can find a related example in your book too ^_^