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Answer :
Answer:
3.79 J
Explanation:
The elastic potential energy (EE) stored in the spring is equal to half of the spring constant (k) times the square of the displacement (Δx). To find how far the spring is displaced, we can use Hooke's law. This law says that the force on the spring (F) is equal to the product of the spring constant (k) and the displacement (Δx).
Hooke's Law
First, let's use Hooke's law to find how far the spring is displaced. The force on the spring is equal to the weight of the object hanging from it (mg).
[tex]\Large \text {$ F=k\Delta x $}\\\\\Large \text {$ mg=k\Delta x $}\\\\\Large \text {$ (3\ kg)(9.8\ N/kg)=(114\ N/m)\Delta x $}\\\\\Large \text {$ \Delta x=0.258\ m $}[/tex]
Elastic Energy
Now we can find the amount of elastic potential energy.
[tex]\Large \text {$ EE=\frac{1}{2}k{\Delta x}^2 $}\\\\\Large \text {$ EE=\frac{1}{2}(114\ N/m)(0.258\ m)^2 $}\\\\\Large \text {$ EE=3.79\ J $}[/tex]
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