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For what angle is horizontal speed fastest -- How measure ramp angle?

  1. Sep 18, 2015 #1
    Hi! I'd just please like to know the most efficient way to conduct my experiment.

    See, my research question is "for what angle is horizontal speed the fastest?"

    We all know that the steeper a hill is, the faster an object accelerates. Obviously a 90 degree angle won't do much.
    I will try to mimic that phenomenon using a small scale experiment.

    I'd be using a toy car and a wooden block i can readily incline as I deem fit. I'll be measuring the speed and so on.

    My question is, how do I measure the angle of inclination accurately? Must I use a huge protractor?
  2. jcsd
  3. Sep 18, 2015 #2
    A protractor is a simple and purpose made instrument for measuring angles, but there is no reason why it would have to be huge.
  4. Sep 18, 2015 #3


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  5. Sep 18, 2015 #4


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    Why not simply measure lengths?
    (The height difference of the ramp ends) / (length of ramp) = sin(slope)

    Eg. a 1m ramp with one end 10cm above the other has a slope of arcsin( 0.1) = 5.7o
  6. Sep 19, 2015 #5


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    Slight mistake, it's rise over run = ##tan(\theta)##.

    PS. Actually, a huge protractor is not a bad idea, it could work perfectly well.
    Last edited: Sep 19, 2015
  7. Sep 19, 2015 #6


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    Yes, I did think about that way. But OP asked about angle of slope.

    I thought the easier measurement, which would be a constant rather than a varying value, is the length along the slope. This is the hypoteneuse: hence the use of sine.

    If you measure " rise over run = tan(θ) " then for each slope you will have to drop a plumbline or something from the top end and make two measurements. (Though perhaps you could have a fixed height block, lay your ramp on that and the floor and slide the foot incrementally nearer to the block. This seems a bit less convenient and I did my way in preference.)

    I'm not sure how "slope" is defined (if at all), but if you do want to use the tangent, as many people do, it is just a mathematical conversion of the angle.
    Similarly, if you want the slope with respect to the vertical, just use cos instead of sin.

    If you know what you want, it's all just maths. My point was simply that measuring lengths is often more convenient than measuring angles - eg. engineers' sine blocks/bars.
  8. Sep 19, 2015 #7
    But rise over hypotenuse is sin(theta).

    Edit: I posted before Merlin replied, so excuse the redundancy.
  9. Sep 19, 2015 #8


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    Sorry, I assumed the car was being released from a fixed height. So measuring the height would be necessary anyway, and the slope length would vary. I guess we have different ideas of what the experiment is going to be.

    Actually, that sliding block idea seems to be a most convenient one for an experiment like this that has a fixed height.
    Last edited: Sep 19, 2015
  10. Sep 19, 2015 #9


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    So okay, to apply some engineering insight to this. One will have to have something like a ramp and a block. One could also use a vice. But a block makes it quite easy if one has for example 10 bricks. Bricks can be placed at the base of the plank, in each corner, so that the car goes between them. Bricks can form the block or hold it in place. This system could be quite tunable for angles. A big protractor could work or one could do the measurements. For me, the measurements are easier, one could even use a spreadsheet to avoid doing any heavy calculations.

    The block could be reduced in size by removing bricks, allowing shallow angles to be set up. This block and plank idea looks very doable to me.
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