This was a question my friend found in a book.
A block attached to a spring pulled by a constant horizontal force is kept on a smooth horizontal surface. Initially the spring is in its natural state. Then the maximum work that the applied force F can do is:
My friend thought that the answer is (a) since the maximum displacement is $x=F/k$ and $W=Fx=F^2/k$. But he saw that the book's answer is different and he asked this question to me.
I at first thought that the answer will be (a), but then I realised that this situation is somewhat similar to a charging capacitor. The final energy of the spring is actually $\frac12kx^2=F^2/2k$. So probably the answer is (d)? But the work done is still (a)? But the book says neither. It's (b). This is the logic in the book:
Method 1: in the book:
(since the book is an objective questions book it did not have detailed explanations)
What is wrong in the following methods?
Method 2: by calculating the maximum displacement
Method 3: by calculating the final energy
PS: We both know calculus so don't hesitate to use it in the answers.