# If the length of a 19 cm spring increases to 54 cm when a 4 kg weight is hanging from it, what is the spring's constant?

Oct 27, 2017

The spring constant is 112 N/m.

#### Explanation:

Spring constant it typically given in units of N/m, so I will convert the spring lengths to m. 19 cm = 0.19 m & 54 cm = 0.54 m

The weight of that 4 kg mass is $m \cdot g = 4 k g \cdot 9.8 \frac{m}{s} ^ 2 = 39.2 N$.
The amount of stretch that the weight caused was
$0.54 m - 0.19 m = 0.35 m$

Therefore the spring constant is $\frac{39.2 N}{0.35 m} = 112 \frac{N}{m}$

I hope this helps,
Steve