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I have been assigned to build a ramp for a small car. I have only one A2 sheet of paper, scissors and a stapler. What would be the best slope profile, in order to move the car as far as possible after leaving the ramp, using only gravity? Any other ideas on construction?

The car is 1:43 size. The weight is 100 g. The car must stay on the track and there is no initial push.

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    $\begingroup$ You need to provide additional details about the exercise for this to be a meaningful question. How much does the car weigh, and what are the dimensions of the car? Are you allowed to push start the car, or is it strictly gravity driven? Are points docked if the car falls over the side of the track? How is the track expected to remain in place? ... $\endgroup$ – user16 Jun 16 '15 at 11:38
  • $\begingroup$ When you say track, do you mean the car needs to be able to perform a loop within the paper (which is impossible, since you'll need to start on a downwards slope and your car will lose kinetic energy to friction and won't be able to make it to the top again at the end of the loop)? Or can it be a ramp which speeds the car up and then the car moves on a table or something? $\endgroup$ – Wasabi Jun 16 '15 at 12:26
  • $\begingroup$ Yes, it's a ramp. It should just go from A to B in a straight line, using only gravity $\endgroup$ – Trenera Jun 16 '15 at 12:27
  • $\begingroup$ Are you building a ramp or a track? The difference being that a ramp starts the car, then the car leaves the ramp. A track would be something that the car never leaves. I am confused about whether you are going for total rolling distance on a hard surface or something like a rollercoaster. $\endgroup$ – hazzey Jun 16 '15 at 12:58
  • $\begingroup$ I need the ramp, just to start the car. Afterwards it should leave the track in order to go the maximum distance from start point $\endgroup$ – Trenera Jun 16 '15 at 13:02
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So there's a number of concerns that you want to think about. Some of these you'll have to determine experimentally, others you'll be able to calculate and then iteratively improve based upon your observations.

It should be understood / obvious that the higher up you can get the car, then the faster it will be able to go, and ultimately travel the furthest distance. The challenge though is transferring the vertical potential energy into horizontal motion. So the taller and longer of a ramp you can make, then the furthest your car will end up traveling.

Use a fixed, rigid plate to form the initial ramp. Run some experiments to determine the steepest angle the plate can form but still allow the car to roll smoothly off of the ramp. Having the car crash at the end of the ramp doesn't do you any good and wastes any energy that was converted.

Once you know your angle of attack for the ramp, you'll want to start experimenting with various ramp designs. This is where the principles of beam deflection start coming into play.

I'd look into C and I (or H) beams as they ought to provide optimal stiffness at the edges of the beams while minimizing the amount of material required. An H beam design may allow you to join two beams together and fasten them in areas where the car won't be impacted by the staples. Another advantage of those beams is that they'll provide rails to keep the car on the track. That said, you'll need to fold under the edges of the H beam where the ramp meets the horizontal surface the car will travel along.

Likewise, look into triangular beams to create the struts that will support and lift your ramp up into the air.

If you'd like to do some of the beam calculations ahead of time, it's pretty easy to search for Young's modulus of elasticity for paper. That parameter can be affected by paper weight and coating, so that's research you'll want to do on your own.

Knowing the angle of attack and your preferred beam design will allow you to lay things out on the sheet of A2 paper that you have. This represents your final constraint inasmuch as you have a fixed amount of material you can use.

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  • $\begingroup$ We had a contest in mechanical engineering class to build a bridge out of paper. Whose bridge could support the most weight would win... First we used really thick paper (like 120g/m^2) and the second (most valuable) info you can get: paper can't take shear stress very well, so try to roll it up for creating struts or fold it to make stiffeners. The model which won was three rolled up papers joined in one point which supported the weight. $\endgroup$ – Knigge46 Jun 19 '15 at 11:53

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