Question

A spring is hanging from the ceiling. When a 2 kg mass is hung from the spring, the spring has a total length of 50 cm. When a 5 kg mass is hung from the spring, the spring has a total length of 70 cm.

Determine the spring's relaxed length and its spring's spring constant. (You should keep 4 decimals in your values to avoid rounding errors.)

Answer 1

here

F = k * x

k = F / x

k = 2 * 9.8 / (50 - x) --------------------(1)

then

k = F / x

k = 5 *9.8 / (70 - x) ----------------------------(2)

from 1 and 2

2 * 9.8 / (50 - x) = 5 *9.8 / (70 - x)

x = 36.67 cm

the relaxed length is 36.67 cm

then the spring's constant is

k = 2 * 9.8 / (0.50 - 0.3667)

k = 147.036 N/m