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

12.8cm

Step-by-step explanation:

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

Answer 2

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

(a) is correct option

Step-by-step 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=(mg)/(k)`

For three masses,

`\Delta x=(3mg)/(k)`

Put the value into the formula

`\Delta x=(3*6.4*9.8)/(7.8*10^(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