Final answer:
To calculate the elastic potential energy stored in a spring when its length is 8 cm, we use the formula U = ½ k x², where k is the spring constant (51.0 N/m) and x is the displacement (0.035 m). The calculated potential energy is 0.0314 joules.
Step-by-step explanation:
The student's question pertains to the elastic potential energy stored in a spring, which is a topic covered in high school Physics. To find the elastic potential energy stored in the spring when its length is 8 cm, we can use the elastic potential energy formula:
U = ½ k x²
where U is the elastic potential energy, k is the spring constant, and x is the displacement from the spring's relaxed length.
In this case, the relaxed length is 11.5 cm and the spring is compressed to 8 cm, so the displacement x:
x = 11.5 cm - 8 cm
x = 3.5 cm or 0.035 m.
The spring constant k is given as 51.0 N/m.
Plugging the values into the formula yields:
U = ½ × 51.0 N/m × (0.035 m)²
After calculations, the elastic potential energy U comes out to be:
U = 0.0314 J
Therefore, the spring stores 0.0314 joules of elastic potential energy when compressed to a length of 8 cm.