| Mechanics > Work and Energy > Conservation of Energy |
DCS# 1M40.20 |
LOOP THE LOOP
-
APPARATUS
| loop the loop track |
202-13-F |
| plastic ball |
202-14-E5 |
| meter stick |
101-05-F |
DESCRIPTION
Calculate
the minimum height from
which
the ball must be released in order to make it through loop and then
verify this experimentally.
NOTES
potential energy
at initial
height = translational + rotational + potential energy at top of loop
mgh = 1/2 I ω2 + 1/2 mv2
+ mg2(R-r)
- substitute:
- I
= 2/5 mr2 for
a solid sphere
ω= v/r,
assuming ball makes contact with bottom rather than edges of track
v2
= g/(R-r)
since gravity provides centripetal force at the top of the loop
h =
2.7(R-r)