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Calculating the Component of the weight that acts along a line

  1. Jan 28, 2017 #1
    1. The problem statement, all variables and given/known data
    A cyclist rides along a road up an incline at a steady speed of 9.0 m s–1. The mass of the rider and bicycle is 70kg and the bicycle travels 15 m along the road for every 1.0 m gained in height. Neglect energy loss due to frictional forces.

    Calculate the component of the weight of the bicycle and the rider that acts along the incline.

    2. Relevant equations

    sinθ=opp/hyp, not sure what else I need to use

    3. The attempt at a solution

    Apparently the answer is 46N but I'm really not sure how to get to that. I found an angle of 3.8 degrees by doing 1.0/15 but I'm not sure where to go from there. The Mark scheme says F=sinθ=Wx1.0/15 I don't quite understand what it's saying.

    Thanks
     
  2. jcsd
  3. Jan 28, 2017 #2

    CWatters

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    Try drawing a diagram showing the weight vector. Then resolve the weight vector into two components, one parallel with the incline and one perpendicular to the incline.
     
  4. Jan 28, 2017 #3

    CWatters

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    I think that's wrong. It should say..

    F = W * sin(θ) = W * 1.0/15
     
  5. Jan 28, 2017 #4
    Yeah I did try that but ended up with 4.6 not 46. I did Sin3.8*70 and got 4.6 so I'm not sure if my angle is wrong?
     
  6. Jan 28, 2017 #5
    Ah ok thanks
     
  7. Jan 28, 2017 #6
    I think every incline problem should start with a sketch, something like the attached file. 3.8 degrees is correct and you found that by knowing the sine of the angle is the sin = opp/hyp = 1.0/15. Referring to the attached pic, if you know W, (the hypotenuse) how do you calculate the opposite side (assuming phi is the angle) of the triangle?
     

    Attached Files:

  8. Jan 28, 2017 #7
    I assume you'd do Sin3.8*70 as in Opp=Sinθ*hyp however that left me with the answer 4.6 not 46.
    (thanks for helping btw)
     
  9. Jan 28, 2017 #8
    What does the force, W equal in terms of the mass, m? W=m x _____
     
  10. Jan 28, 2017 #9
    Oh of course mass doesn't taken into account gravity, I understand now. Thank you!!!
     
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