3 questions about Spring constant equation

1. A spring in free suspension has a length of 10 cm. At the free end, a 200 gram weight is suspended so that the length of the spring is 11 cm. If g = 10 m/s^{2}, what is the spring force constant?

__Known:__

The initial length of the spring (y_{1}) = 10 cm = 0.10 m

The final length of the spring (y_{2}) = 11 cm = 0.11 m

Spring length change (Δy) = 0.11 – 0.10 = 0.01 meter

The mass of the load (m) = 200 grams = 0.2 kg

Load weight (w) = m g = (0,2)(10) = 2 Newtons

__Wanted:__ Spring constant (k)

__Solution:__

Spring constant formula:

F = k Δy

k = F / Δy = 2 / 0,01 = 200 / 1 = 200 Newton/meter

2. A spring can be stretched so that it is extended by 10 cm with a potential energy of 0.5 Joule. What is the spring constant?

__Known:__

The addition of the spring length (Δy) = 10 cm = 0.1 meter

Spring potential energy (EP) = 0.5 Joule

__Wanted:__ Spring constant (k)

__Solution:__

The spring constant is calculated using the Spring Potential Energy formula:

EP = ½ k Δy^{2}

2 EP = k Δy^{2}

2 (0,5) = k (0,1)^{2}

1 = k (0,01)

k = 1 / 0,01 = 100 / 1 = 100 Newton/meter

3. A spring pulled with a force of 100 N increases its length by 5 cm. Calculate the spring constant.

__Known:__

Force (F) = 100 N

Increase in spring length (Δx) = 5 cm = 0.05 m

__Wanted:__ Spring constant (k)

__Solution:__

F = k Δx

k = F / Δx = 100 / 0,05 = 10.000 / 5 = 2000 Newton/meter