SOLUTION: I am having difficulty with this. Please help. if a pendulum has a period of 2 seconds, find its length rounded to the nearest tenth of a foot use formula T= 2 pi sqrt L/32

Algebra ->  Rational-functions -> SOLUTION: I am having difficulty with this. Please help. if a pendulum has a period of 2 seconds, find its length rounded to the nearest tenth of a foot use formula T= 2 pi sqrt L/32      Log On


   

Question 320096: I am having difficulty with this. Please help.
if a pendulum has a period of 2 seconds, find its length rounded to the nearest tenth of a foot use formula T= 2 pi sqrt L/32
Found 2 solutions by vleith, Theo:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
T=+2%2Api%2Asqrt%28L%2F32%29
Given T = 2 , find L
2=+2%2Api%2Asqrt%28L%2F32%29
2%2F%282%2Api%29+=+sqrt%28L%2F32%29
1%2Fpi+=+sqrt%28L%2F32%29
0.318+=+sqrt%28L%2F32%29
%280.318%29%5E2+=+L%2F32
32+%2A+%280.318%29%5E2+=+L
3.24+=+L
rounded to nearest tenth 3.2 feet
Check your answer

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
The formula is T = 2*pi*sqrt(L/32) if I read it correctly.

The general formula is T = 2*pi*sqrt(L/g)

T is the period in seconds and L is the length of the pendulum in feet.

The acceleration of gravity is given as approximately 32 feet per second squared.

Since you know T, then you have to solve for L.

Replace T with 2 to make your formula equal to:

2 = 2*pi*sqrt(L/32)

Divide both sides of this equation by 2*pi to get:

2/(2*pi) = sqrt(L/32)

Simplify this to get:

(1/pi) = sqrt(L/32)

Square both sides of this equation to get:

(1/pi)^2 = L/32

Simplify this to get:

1/pi^2 = L/32

Multiply both sides of this equation by 32 to get:

32/pi^2 = L

Solve for L to get:

L = 3.242277877 feet which is roughly 3.24 feet.

This assumes that the acceleration due to gravity is 32 feet per second squared.

The actual acceleration due to gravity is closer to 32.2 feet per second squared.

If the length of the pendulum is given in feet, then use the acceleration of gravity as 32 feet per second squared as shown in your problem.

If the length of the pendulum was given in meters, then the formula that needed to be used was the acceleration of gravity in meters per second squared.

That would have been roughly 9.8 meters per second squared.

Any discrepancy in between meters and feet is due to rounding errors.

You can use the following online calculator to check your answer.

http://www.easycalculation.com/physics/classical-physics/simple-pendulum.php

This tool works in meters, so you need to convert your figures from feet to meters.

32 feet per second squared is roughly equivalent to 9.75 meters per second squared.

You tell the tool that you want to solve for L.

You enter 9.75 in the acceleration of gravity field.

You enter 2 in the period field.

You will get an answer of .99 meters for the length of the pendulum.

You multiply .99 by 3.28 to get 3.2472 feet.

My answer was 3.2422 feet.

The difference is in rounding.

The tool is useful to tell you if you're close to the right answer but not good to tell you whether you were right on because it rounds to 2 decimal places.

I used it to confirm my answer was close to what should have been expected.

Your answer should be L = 3.24 feet given the accuracy of the data you were provided: