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makkiz [27]
3 years ago
8

Inthisexperiment,aspringforcewasusedtokeep moving object travelingin a circularpath.The size of a spring force should be proport

ional to the amount of stretch in the spring. Doesthisclaimagree qualitatively with the data in your five trials? Why or why not?
Physics
1 answer:
poizon [28]3 years ago
3 0

Answer:

By calculation, it can be shown that;

K = \frac{F_{angular}}{2\times x\times c}

Whereby for constant K, as  {F_{angular}} 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

\frac{1}{2}\cdot k\cdot x^2.

Rotational kinetic energy = \frac{1}{2}·I·ω²

Inertia,  I =  \frac{1}{2}·m·r²

ω = \frac{v}{r}

Substituting gives

Rotational kinetic energy =  \frac{1}{2}·

=  \frac{1}{4}·m· v²

Equating both equations gives

K = \frac{2\times m\times v^2}{4\times x^{2} }  = \frac{1\times m\times v^2}{2\times x^{2} }  

Within the proportionality limit, x ∝ r

therefore we can write x = c·r which gives

\frac{ m\times v^2}{2\times x\times c\times r } = \frac{v^{2} }{r} \times\frac{m}{2\times x\times c}

Since \frac{v^{2} }{r} = angular acceleration, α, then

m× \frac{v^{2} }{r} = Angular force

Therefore K = \frac{F_{angular}}{2\times x\times c}

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.

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