physics science fair project. Need help fastt!!!?
So tomorrow I have my science fair project presentation and my project is a roller coaster made out of materials I found in my house that were reliable to make an appropriate project. My "roller coaster" consisted of a 4 feet high starting point and a loop that was adjustable to any radius ranging from 5 inches to 6.5 inches. My question is "how does the radius of a circular loop affect the speed required for an object(marble) to complete the circular loop?" I tested 4 radius that were 6.5 in, 6 in, 5.5 in, and 5 in. I found the heights that each individual radius require the object to have in order to complete the loop but I'm still not sure how to conclude how the speed is affected by the radius of the loop. Can I get some helpp please!
My results were:
Radius 6.5 in = height of 1.8 ft
Radius 6 = height of 1.6 ft
Radius 5.5 = height of 1.4 ft
Radius 5 in = height if 1.25 ft
- 7 years agoFavorite Answer
this is an energy question
the potential energy at the starting h is M*g*h
the kinetic energy at the top of the loop is 1/2 *m*v^2
the potential energy must be such that KE is greater than zero at the top of the loop, at least!
the height drop from the starting point to the top of the loop is the only dependance in an ideal world, the radius does not matter. So as long as the starting point is just above the top of the loop, h>0, the rollercoaster will complete the loop. However, there's a big difference in yours, that's due to friction between the cart and track.
In you equations:
total energy = mgh
total energy =1/2mv^2
h is proportional to v^2, g and m are constant
the 'extra h' is the frictional energy to be over come which is simply:
where, h is the starting height above the top of the loop
you can go into more detail if you want here:
and there's a niceanimation of what I explained here:
- TechnobuffLv 77 years ago
I don't know how you arrived at launch heights, but what you should do is for each radius of loop, reduce the height and repeat the launch until the marble comes free of the track at the top of the loop. Then increase the start height gently until the marble is able to complete the loop without unsticking at the top. That is the minimum launch height for each radius change.
Your figures may well be right if you followed such a procedure, but if not, start again.
- arrandaLv 44 years ago
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