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/s2, what is the spring force constant?
Known:
The initial length of the spring (y1) = 10 cm = 0.10 m
The final length of the spring (y2) = 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 Δy2
2 EP = k Δy2
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
