What is the Correct Equation for Calculating the Length of a Spring?

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The discussion centers on the correct equation for calculating the length of a spring, with an initial attempt using energy and force equations leading to confusion. The user derived the equation √(2mg/k) = x but found it did not match the provided answer choices. A key point raised is the incorrect comparison of force and energy in the user's calculations. Additionally, the frequency of a mass on a spring and a simple pendulum were compared, revealing discrepancies in the derived formulas. The final clarification emphasizes that the angular frequency (ω) must be converted to frequency (f) by dividing by 2π, explaining the missing factor in the answer.
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Homework Statement


http://img26.imageshack.us/i/1113001.jpg/

#12


Homework Equations



u=(1/2)kx^2
F=mg

The Attempt at a Solution



mg=(1/2)kx^2
√(2mg/k) = x

however, this is not any of the choices.
the correct answer is B)mg/k
 
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dinhjeffrey said:
mg=(1/2)kx^2
:confused: You seem to be setting a force equal to an energy. Not good.

What's the frequency of a mass on a spring? Of a simple pendulum? Compare.
 
okay i got the frequency of a mass of a spring is
f=√(g/L)/2π
and of a simple pendulum
w=√(k/m)

if i set them equal to each other i get
L = mg/(2πk) which is almost right, but the 2π is disregarded in the answer. does anyone know why?
 
ω is the angular frequency, not the frequency. To get f from ω, divide by 2pi.
 
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Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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