Math: Applications of Dot Product

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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+++++Please provide a step by step solution to this problem (question 15)! I really don't know what I'm doing! I know the answer, but I don't know how to get that answer! Thank you.

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  1. 14)
    F vector at 40 degrees to motion direction Call Unit vector up ramp parallel to ramp Au.
    The component of F in the direction of Au is
    F dot Au = |F| * 1 cos (40) = 125(.766) = 95.8 Newtons

    15) The 125 N is at 20+40 = 60 degrees from horizonal, so at 30 degrees from vertical
    125 cos 30 = 108.3 N

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