Three identical 6.4kg masses are hung by three identical springs. Each spring has a force constant of 7.8 Kn/m and is 12cm long before any masses are attached to it. how long is the bottom most spring going to be after the three masses are hung on it a. 14.3 b. 16.2 c.12.8 d.10.7

The correct option is;

c. 12.8 cm

Explanation:

The given parameters are;

The length of each spring = 12 m  = 0.12 m

Given that the masses and the springs are vertically oriented, we have;

The mass on the first spring = 3 × 6.4 = 19.2 kg

The weight on the first spring = 19.2 kg × 9.81 m/s² = 188.352 N

The extension of the first spring = 188.352 N/7,800 N/m ≈ 0.02415 m

The mass on the second spring = 2 × 6.4 = 12.8 kg

The weight on the second spring = 12.8 kg × 9.81 m/s² = 125.568 N

The extension of the second spring = 125.568 N/7,800 N/m ≈ 0.016098 m

The mass on the third spring = 1 × 6.4 = 6.4 kg

The weight on the third spring = 6.4 kg × 9.81 m/s² = 62.784 N

The extension of the third (bottom) spring = 62.784 N/7,800 N/m ≈ 0.00805 m

The total length of the bottom spring = Original length of the bottom spring + Extension of the bottom spring

The total length of the bottom spring ≈ 0.12 m + 0.00805 m = 0.12805 m

The total length of the bottom spring ≈ 0.12805 m ≈ 12.81 cm

The bottom spring will be approximately 12.81 cm long.