Answer:
By calculation, it can be shown that;
K =
Whereby for constant K, as increases, x also increases.
Explanation:
The experiment set up consisted of the use of a spring force to maintain the object in circular path.
The energy in the spring is given by
.
Rotational kinetic energy = ·I·ω²
Inertia, I = ·m·r²
ω =
Substituting gives
Rotational kinetic energy = ·
= ·m· v²
Equating both equations gives
K = =
Within the proportionality limit, x ∝ r
therefore we can write x = c·r which gives
=
Since = angular acceleration, α, then
m× = Angular force
Therefore K =
Therefore as Force, F increases, x also increases and the size of a spring force should be proportional to the amount of stretch in the spring.
