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wel
3 years ago
12

The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing

back and forth. What is the length of a pendulum that makes one full swing in 2.2 seconds? Use 3.14 for pi.
Mathematics
2 answers:
madam [21]3 years ago
7 0

Answer:

it is 3 on ed

Step-by-step explanation:

I did it

pantera1 [17]3 years ago
3 0

Remark

I like to work from the original equation.

Givens

T = 2.2 seconds

pi = 3.14

L = ??

Substitute and Solve

T = 2*pi*sqrt(L/32) Find the value of 2*pi

2.2 = 2*3.14* sqrt(L/32)

2.2 = 6.28 * sqrt(L/32) Divide both sides by 6.28

2.2/6.28 = sqrt(L/32)

0.35032 = sqrt(L/32) Square both sides.

0.122723 = L/32 Multiply both sides by 32

0.122723 * 32 = L

L = 3.927 feet. <<<<< Length pendulum creating 2.2 seconds.

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1 year ago
A 140 kg camera is suspended by two wires over a 40 metre wide football field to get shots of the action from above. At one poin
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Answer:

Please red the answer below

Step-by-step explanation:

In order to determine the length of each cable you use the Newton second law for each component of the forces involved in the situation.

For the x component you have:

T_1cos\theta_1-T_2cos\theta_2=0           (1)

T1: tension of the first cable = 1500N

T2: tension of the second cable = 800N

θ1: angle between the horizontal and the first cable

θ2: angle between the horizontal and the first cable

For the y component you have:

T_1sin\theta_1+T_2sin\theta_2-W=0               (2)

W: weight of the camera = Mg = (140kg)(9.8m/s^2) = 1372N

You can squared both equations (1) and (2) and the sum the two equations:

T_1^2cos^2\theta_1=T_2^2cos^2\theta_2\\\\T_1^2sin^2\theta_1=T_2^2sin^2\theta_2-2WT_2sin\theta_2+W^2

Then, you sum the equations:

T_1^2(cos^2\theta_1+sin^2\theta_1)=T_2^2(sin^2\theta_2+cos^2\theta_2)-2Wsin\theta_2+W^2        (3)

Next, you use the following identity:

sin^2\theta+cos^2\theta=1

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T_1^2=T_2^2-2WT_2sin\theta_2+W^2\\\\sin\theta_2=\frac{T_2^2-T_1^2+W^2}{2WT_2}=\frac{(800N)^2-(1500)^2+(1372N)^2}{2(800N)(1372N)}=0.066\\\\\theta_2=sin^{-1}0.066=27.23\°

With this values you can calculate the value of the another angle, by using the equation (1):

\theta_1=cos^{-1}(\frac{T_2cos(27.23\°)}{T_1})=cos^{-1}(\frac{(800N)(cos27.23\°)}{1500N})\\\\\theta_1=61.69\°

Now, you can calculate the length of each cable by using the information about the width of the football field. You use the following trigonometric relation:

l_1cos\theta_1=40-d\\\\l_2cos\theta_2=d\\\\

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3 years ago
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Answer:

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Hello,

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