Mylenepantollanoidn
Answered

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Problem: The length of the arc formed by the first swing of the bob of a
pendulum is 20 cm. If each succeeding swing is 3/4 of the preceding one,
a. how far will it travel in the first six swings?
b. how far will it travel before it comes to rest?​

Sagot :

KallesEliasidn

Problem:

The length of the arc formed by the first swing of the bob of a pendulum is 20 cm. If each succeeding swing is 3/4 of the preceding one,

a. how far will it travel in the first six swings?

b. how far will it travel before it comes to rest?​

Solution:

a1 = 20 cm

a2 = 20(3/4) = 15 cm

a3 = 15(3/4) = 11.25 cm

a4 = 11.25(3/4) = 8.4375 cm

a5 = 8.4375(3/4) = 6.328125 cm

a6 = 6.328125(3/4) = 4.74609375 cm

a. how far will it travel in the first six swings?

Sum = 20 + 15 + 11.25 + 8.4375 + 6.328125 + 4.74609375

Sum = 65.76171875 cm

It will travel up to 65.76171875 cm in the first six swings

b. how far will it travel before it comes to rest?​

[tex]\[\begin{array}{l}S = \frac{{{a_1}}}{{1 - r}}\\\\S = \frac{{20}}{{1 - (\frac{3}{4})}}\\\\S = \frac{{20}}{{\frac{1}{4}}}\\\\S = 20(4)\\\\S = 80\end{array}\][/tex]

It will travel up to 80 cm before it comes to rest

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