What is work done by a spring force
Answers
Answer:
Elastic potential energy is Potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched.
Explanation:
Hope it will be helpful for you.
Dear student,
We find the work done by spring force with two possible cases. One case could be either the string is stretched or compressed and another one will be if it were to be stretched from some position x₁ to x₂.
We have:
dx = small change in length
∅ = 180° (since spring force acts oppositely)
By formula, we know that:
Fs = Kx
[where, Fs = spring force
K = spring constant
x = change in length ]
Case 1: If the string were to be stretched or compressed.
[ we have; Mean position, x₁ = 0
Final position, x₂ = x ]
W = F.s cos∅
W = Fs . x cos∅
dW = Fs. dx cos∅
∫dW = ∫Kx.dx cos180°
W = - K∫(x²/2)
W = - 1/2 Kx²
Case 2: If the string were to be stretched from one position to x₁ to another position x₂.
[ we have: first position = x₁
second position = x₂ ]
W = F.s cos∅
W = Fs . x cos∅
dW = Fs. dx cos∅
∫dW = ∫(Kx.dx cos180°) from x₁ to x₂
W = - K(x²/2) from x₁ to x₂
W = - 1/2 K (x₂² - x₁²)
Hence, the possible values of the work done depend upon whether they were stretched from mean position to some position or from already stretched/compressed position to another stretched/compressed position i.e.
W = - 1/2 Kx²
or W = - 1/2 K (x₂² - x₁²)
