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A unstretched spring hangs from the ceiling with a length of 0.31 m. a 9.1-kg block is hung from the spring and the spring stretches to be 0.50 m long. how long will the spring be if a 3.3-kg block is hung from the spring? for both cases, all vibrations of the spring are allowed to settle down before any measurements are made.

Respuesta :

As we know that spring force is given by

[tex]F = kx[/tex]

here we know that for the equilibrium of the mass suspended with the spring we have

[tex]mg = kx[/tex]

so now we have

[tex]9.1(9.81) = k(0.50 -0.31)[/tex]

now we have

[tex]k = 469.8 N/m[/tex]

now we have another mass

m = 3.3 kg

again from above equation we have

[tex]3.3 (9.81) = 469.8(L - 0.31)[/tex]

[tex]L = 0.38 m[/tex]

so final length of the spring will be 0.38 m

onyebuchinnaji

When the mass is changed to 3.3 kg, the length of the spring is 0.38 m.

Spring constant

The spring constant of the spring is calculated as follows;

F = kx

mg = kx

k = mg/x

k = (9.1 x 9.8) / (0.5 - 0.31)

k = 469.4 N/m

New length of the spring

When the mass is changed to 3.3 kg, the length of the spring is calculated as follows;

k = mg/x

x = mg/k

x = (3.3 x 9.8)/469.4

x = 0.07

New length, = 0.31 + x = 0.31 + 0.07 = 0.38 m

Learn more about Hooke's law here: https://brainly.com/question/2648431

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