Help rearranging this equation.

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AI Thread Summary
To find the length of a steel beam swinging with a period of 5.00 seconds, the equation T=2pi*sqrt(L/g)*(sqrt2/3) is used. The user attempted to rearrange it to L=sqrt[g*(T/(2pi*sqrt(2/3)))] but seeks confirmation and assistance. A suggestion was made to square both sides of the original equation for a more straightforward approach. The user is encouraged to substitute known values into the rearranged equation for a solution. The discussion focuses on solving for the length using the correct mathematical manipulation of the given formula.
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Homework Statement


On the construction site for a new skyscraper, a uniform beam of steel is suspended from one end. If the beam swings back and forth with a period of 5.00 , what is its length?

I know the equation I need to use but I'm having trouble rearranging it to solve for Length (L).



Homework Equations


T=2pi*sqrt(L/g)*(sqrt2/3)


The Attempt at a Solution


I tried to rearrange the equation to solve for L and got this.
L=sqrt[g*(T/(2pi*sqrt(2/3)))]

any help would be great!
 
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Welcome to PF.

Why not simply square both sides of the original?

You know all the other values. Plug them in.
 
Thread 'Variable mass system : water sprayed into a moving container'

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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