To find the potential energy stored in a compressed spring, we can use the formula for elastic potential energy:
[tex]\[ PE = \frac{1}{2} k x^2 \][/tex]
where [tex]\( PE \)[/tex] is the potential energy, [tex]\( k \)[/tex] is the spring constant, and [tex]\( x \)[/tex] is the displacement (compression) of the spring.
Given the values:
- Displacement, [tex]\( x = 0.65 \)[/tex] meters
- Spring constant, [tex]\( k = 95 \)[/tex] N/m
We can now substitute these values into the formula:
[tex]\[ PE = \frac{1}{2} \times 95 \times (0.65)^2 \][/tex]
First, calculate [tex]\( x^2 \)[/tex]:
[tex]\[ (0.65)^2 = 0.4225 \][/tex]
Next, multiply this value by the spring constant [tex]\( k \)[/tex]:
[tex]\[ 95 \times 0.4225 = 40.1375 \][/tex]
Then, multiply by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ \frac{1}{2} \times 40.1375 = 20.06875 \][/tex]
Therefore, the potential energy stored in the spring is approximately 20 J.
So, the correct answer is:
[tex]\[ \boxed{20 \text{ J}} \][/tex]
