# In a room that is 2.13 m high, a spring (unstrained length = 0.30 m) hangs from the ceiling. A board whose length is 1.58 m is attached to the free end of the spring. The board hangs straight down, so that its 1.58-m length is perpendicular to the floor. The weight of the board (115 N) stretches the spring so that the lower end of the board just extends to, but does not touch, the floor. What is the spring constant of the spring?

the stretched length of the spring is

2.13 - 1.59 -.30

check that.

k= weight/stretched length

## To find the spring constant of the spring, you need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Here's how you can find the spring constant step by step:

1. Find the stretched length of the spring:
- The total height of the room is 2.13 m.
- The length of the board is 1.58 m.
- The unstrained length of the spring is 0.30 m.
- Subtract the length of the board and the unstrained length of the spring from the total height of the room:
Stretched length = 2.13 m - 1.58 m - 0.30 m = 0.25 m

2. Calculate the spring constant (k) using the formula:
k = weight / stretched length
- The weight of the board is given as 115 N.
- The stretched length of the spring is 0.25 m.
- Substitute the values into the formula:
k = 115 N / 0.25 m ≈ 460 N/m

So, the spring constant of the spring is approximately 460 N/m.