Astronauts visiting planet x have a 250-cm-long string whose mass is 5.00 g. they tie the string to a support, stretch it horizontally over a pulley 2.00 m away, and hang a 4.00 kg mass on the free end. then, the astronauts begin to excite standing waves on the horizontal portion of the string. their data are as follows:

Question

Physics

Mountain

6 January, 17:22

Astronauts visiting planet x have a 250-cm-long string whose mass is 5.00 g. they tie the string to a support, stretch it horizontally over a pulley 2.00 m away, and hang a 4.00 kg mass on the free end. then, the astronauts begin to excite standing waves on the horizontal portion of the string. their data are as follows:

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Selina Waller · Answer 1

The solution for this problem is:

v = sqrt (T/µ) where T = m*g = 4*g and µ = 0.0055/2.5 = 0.0022kg/m

Now L = 2 m

For a string the frequencies are n*v/2L

so n*v/2L = 64 and (n+1) * v/2L = 80

Now eqn 2 divided by eqn 1 yields (n + 1) / n = 80/64 = 1.25

=> 1.25 n = n + 1 or. 25n = 1 or n = 4

now subbing back into eqn 1 we have 4*v/2L = 64 or v = 32*L = 32*1.9 = 60.8

So 60.8 = sqrt (1.1*g/0.0022)

so 1.1*g = 60.8^2*0.0022 = > g = 60.8^2*0.0022/1.1 = 7.39 m/s^2