To simplify our calculations, we decided to launch our ball bearing at an angle of 0 degrees, or flat. To figure out how long and how tall to make our ramp, we played around with our track (the two tubes taped together) to test different heights and inclines. After much trial and error, we eventually found that a height of 142 cm (56 in) and a length of 145 cm (57 in) achieved the greatest distance.
After cutting the 2x4s into the above mentioned lengths, we nailed them together to create the framework of our ramp. We also attached two small supports at the bottom made out of scrap wood to make it more stable (measured 18 in x 0.75 in). We then attached the tubing together side by side by taping the backs (we had to make some adjustments to make the tubing longer by taping extensions on- final length was 84 in) and attached the ends to the ends of the ramp. We then added another support piece made out of scrap wood (measured 4 ft x 0.75 in) at a diagonal so that the curve of the track was supported.
Step 2- Find the average point
The ball was expected to land approximately 6 ft from the end of the ramp. To meet this requirement we used a piano stand and a hot tub to raise the overall height of the ramp until the ball traveled about 6 ft (final height was about 107 in).
In order to make our final calculations, we needed to find the average point that the ball lands in. We did this by drawing and arbitrary coordinate system on a piece of paper, and then taping another piece of paper that had pencil covering the back on top of it. (When we experimented outside, we used a cutting board to put underneath the paper to create a hard surface). We then placed the paper at about 6 ft away from the ramp, and did 20 trial runs. Then we observed the markings left on our coordinate system and calculated the average point. This allowed us to draw a line on the ground that follows the exact path of the ball for placement of a target ring, and determines how far the ball will travel.
Step 3- Calculate the initial velocity
The last step before the final testing of the ramp is to calculate the initial velocity that the ball leaves the origin at. This can be done by measuring the height of the origin (where the ball leaves the ramp) and the distance the ball travels in the x direction.
The values that are highlighted in the picture are the constants of the experiment: height of the origin, displacement in x, and initial velocity in the x direction. These will be used in the final test to calculate an x value when given a y value or vice versa. (Equations come from the Physics Background section).