Answer:
Part A : k = k₁+k₂
Part B: k = k₁+k₂+.....kₙk₃
Where for 3 springs n= 3
Explanation:
Hooke's law states that the force required to stretch a spring is directly proportional to the distance x, where k is the spring constant.
Mathematically, Hooke's law is represented as
F = kx
Where F = Force required to stretch the spring
k = spring constant
x = distance
Part A:
Since the two massless springs in Part A are connected in parallel, it means they are stretched by the same Force (F)
Therefore using Hooke's law
F = kx ......... Equation 1
Total Force is represented by F
Spring 1 , F₁= k₁x ....... Equation 2
Spring 2, F₂= k₂x ......... Equation 3
Total Force = F₁ + F₂ .......... Equation 4
We substitute k₁x for F₁ and k₂x for F₂ in equation 4
F= k₁x+k₂x ........ Equation 5
F = (k₁+k₂)x ........ Equation 6
According to Hooke's law, F = kx
We substitute kx for F in Equation 6
Hence, kx = (k₁+k₂)x ........... Equation 7
Therefore, the Effective springs constant for two massless spring connected in parallel is given as
k = k₁+k₂