How can you determine the height of a building knowing only the period of a simple pendulum?

Question

I'm having trouble with this. I thought I could set .5mv^2 = mgh and find the height of the building by cancelling out mass because I'm not given the mass of the pendulum, but v max = 2piA/T and I can't think of a way to either get rid of A or solve for it. I can't help but feel like I need more information, but all I know is the period (and the acceleration of gravity of course).

Answer 1

T = 2π √(L/g)



L = g T²/(4π²)





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Make a simple pendulum whose length equals the height of the simple pendulum.

Measure the period and find its height using the period.

(Of course one can measure the length of the pendulum directly using measuring tap)

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Answer 2

i'm assuming you have an eye fixed fastened or something to degree time. if so, carry the pendulum from the ceiling of the room with length such that the element mass very almost touches the floor. degree its term. understanding the equation of term for an straight forward pendulum, T = 2*pi*sqrt(L/g) as a results of fact g (accel as a results of grav) is commonly used, and T is measured, we are able to calculate L, that's the dimensions of the pendulum that's additionally equivalent to the peak of the room.

Answer 3

kuiperbelt2003's answer is one way, but as he points out, very difficult because of the extremely small difference in the period measured at the top and bottom of the building.



Here's a crazier way.



Get a rock and a piece of string as long as the height of the building, go up to the top, dangle the pendulum down to within inches of the ground, and have a friend give the rock a push. Measure the period, T, and you'll have the height by



h = g(T/2π)^2

Answer 4

your last phrase is the key....



measure the period and length very accurately, and from this you can calculate the local acceleration due to gravity



the period of a pendulum is



P = 2pi Sqrt[L/g]



squaring both sides and solving for g, you get



g = 4 pi^2 L/P^2



now, the local value of g varies with distance from the center of the earth:



g = GM/r^2 where r is the distance from the center of the earth, G is the newtonian grav constant and M is the mass of the earth



you know that at the surface of the earth, g=9.8m/s/s, so if R is the radius of the earth and h is the height of the building, you can show that



g(at top of building) = 9.8m/s/s (R/(R+h))^2



since R>>h, you will need extremely accurate readings of P and L, but in theory you could measure the height of the building this way