question_answer

A spring of force constant k is cut into two pieces, such that one piece is double the length of the other. What is the force constant of the longer piece of the spring?                             

Answer:

                 Force constant, \[k=\frac{F}{x}\] The length of longer part is\[2x\text{ }/\text{3}\]. So its force constant is \[k'=\frac{F}{2x/3}=\frac{3}{2}\frac{F}{x}=\frac{\mathbf{3}}{\mathbf{2}}\mathbf{k}\].