Question

Three identical 6.4 kg masses are hung by three identical springs as shown. Each spring has a force constant of 7.8kN/m and is 12 cm long before any masses are attached to it. How long is the bottom-most spring going to be after three masses are hung on it?
14.3cm
16.2cm
12.8cm
10.7cm

Answer 1

Answer:

The bottom-most spring going to be after three masses are hung on it is 14.3 cm

(a) is correct option

Explanation:

Given that,

Three identical mass = 6.4 kg

Force constant = 7.8 kN/m

Distance before attached mass = 12 cm

We know that,

When we attached three identical masses then the total mass on the spring will be 3 mg.

We need to find the extension

Using balance equation

$F=mg$

$k\Delta x=mg$

$\Delta x=\dfrac{mg}{k}$

For three masses,

$\Delta x=\dfrac{3mg}{k}$

Put the value into the formula

$\Delta x=\dfrac{3\times6.4\times9.8}{7.8\times10^{3}}$

$\Delta x=0.023\ m$

We need to calculate the length of the bottom spring

Using given length

$x=\Delta x+0.12$

Put the value into the formula

$x=0.023+0.12$

$x=0.143\ m$

$x=14.3\ cm$

Hence, The bottom-most spring going to be after three masses are hung on it is 14.3 cm

(a) is correct option

Answer 2

Answer:

12.8cm

Explanation:

I just took a quiz and got it wrong, so it’s not 14.3, it’s 12.8.