Galileo's Parabolic Experiment - Part #2
In my blog posting of Galileo's Parabolic Experiment - Part #1 https://papercraftetc.blogspot.com/2023/03/a-stem-project-galileos-parabolic.html, I demonstrated Galileo's theory of parabolic trajectory of projectiles. In this posting, I will demonstrate that launching a marble from different heights, changes the amount of kinetic energy as it leaves the ramp. This changes the flight of the marble as shown by the different colored parabolas on the left of the center vertical black line. Higher levels of energy drive the marble further horizontally before it sinks. (The different colored curved lines on the right represent the different height ramps.)
My files contain all of the necessary components to demonstrate this experiment. It can easily be cut by hand, Silhouette, Cricut or another die cutting machine.
I used TurtleStitich to create the ramp. The height of the ramp is the radius of a quarter of a circle. I ran the program three times to create the 3.5, 2.5 and 1.5 inch ramps.
I made a 1 inch circle to simulate the loop in the apparatus in TurtleStitch.
I made a frame to contain the components of the apparatus in TurtleStitch.
To Calculate the Parabola of a free-falling marble
For constant velocity motion, x = vt, where v is velocity and t is time
When an object falls, (g is the acceleration due to gravity), it goes a distance d in time t according to the formula, d = - (1/2)gt2 , (negative because it is dropping).
x = vt d = -1/2 gt2
Substitute t = x/v d = -1/2 g(x/v)2
d = -(g/2v2)x2
g is a constant of 981 cm/sec2
For height of 3.5 in.(8.9 cm.), v = 111.7 cm/sec,
Using the formula, d = -(g/2v2)x2
d = -(.04)x2
Make the Apparatus
Here is the PDF. I used 65 lb. cardstock, one sheet of acetate, Glue Dots and a marble.
Here is the .Studio file.
Here is the SVG. The file extends beyond the scope of the viewing field. Zoom out to see the entire file.
Make the ramps by curving the ramp base and bending the tabs at a right angle (not shown). Apply glue to each tab and adhere the side of the ramp. Repeat for the other side of the ramp. Apply Glue Dots to the back of each ramp. Make the Glue Dots "unsticky" by touching each Glue Dot with your finger about 10 times.
Glue the loop into a circle and apply a glue dot by its seam. Make the Glue Dot "unsticky" by touching the Glue Dot with your finger about 10 times.
Make the Frame
Use the directions from the shuffleboard frame blog posting, https://papercraftetc.blogspot.com/2023/02/a-stem-project-making-shuffleboard-game.html to make the frame.
Assemble the Frame To the Apparatus
Apply glue to the frame.
Apply a few drops of glue to the template. Align the template to the backing.
Add the clear acetate sheet to the front of the template with Glue Dots and adhere to the frame.
Experiment Using a Marble
Place the largest ramp (3.5 inch radius) on the red line on the right. Place the loop in the center of the red line. Release the marble at the top of the red line. The marble will roll down the ramp, follow the trajectory of the red parabolic line and fall through the loop.
Remove the 3.5 inch ramp and loop. Place the medium size ramp (2.5 inch radius) on the green line. Place the loop in the center of the green line. Release the marble at the top of the green line. The marble will roll down the ramp, follow the trajectory of the green parabolic line and fall through the loop.
Remove the 2.5 inch ramp and loop. Place the small size ramp (1.5 inch radius) on the blue line. Place the loop in the center of the blue line. Release the marble at the top of the blue line. The marble will roll down the ramp, follow the trajectory of the blue parabolic line and fall through the loop.
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