Respuesta :
Answer:
The ratio of the energy stored by spring #1 to that stored by spring #2 is 2:1
Explanation:
Let the weight that is hooked to two springs be w.
Spring#1:
Force constant= k
let x1 be the extension in spring#1
Therefore by balancing the forces, we get
Spring force= weight
⇒k·x1=w
⇒x1=w/k
Energy stored in a spring is given by [tex]\frac{1}{2}kx^{2}[/tex] where k is the force constant and x is the extension in spring.
Therefore Energy stored in spring#1 is, [tex]\frac{1}{2}k(x1)^{2}[/tex]
⇒[tex]\frac{1}{2}k(\frac{w}{k})^{2}[/tex]
⇒[tex]\frac{w^{2}}{2k}[/tex]
Spring #2:
Force constant= 2k
let x2 be the extension in spring#2
Therefore by balancing the forces, we get
Spring force= weight
⇒2k·x2=w
⇒x2=w/2k
Therefore Energy stored in spring#2 is, [tex]\frac{1}{2}2k(x2)^{2}[/tex]
⇒[tex]\frac{1}{2}2k(\frac{w}{2k})^{2}[/tex]
⇒[tex]\frac{w^{2}}{4k}[/tex]
∴The ratio of the energy stored by spring #1 to that stored by spring #2 is [tex]\frac{\frac{w^{2}}{2k}}{\frac{w^{2}}{4k}}=[/tex]2:1
