Question

Select the correct answer.
What is the difference between the energy of spring A, stretched 0.6 meters, and spring B, stretched 0.3 meters, if they have the same spring constant?

A.
Spring A has more potential energy than spring B.
B.
Spring A has less potential energy than spring B.
C.
Springs A and B have the same potential energy.
D.
Springs A and B have the same kinetic energy.

Answer 1

The potential energy stored in a spring can be calculated using the formula:

\[
PE = \frac{1}{2} k x^2
\]

where \( PE \) is the potential energy, \( k \) is the spring constant, and \( x \) is the amount of stretch or compression from the spring's equilibrium position.

For Spring A, stretched 0.6 meters:

\[
PE_A = \frac{1}{2} k (0.6)^2 = \frac{1}{2} k (0.36)
\]

For Spring B, stretched 0.3 meters:

\[
PE_B = \frac{1}{2} k (0.3)^2 = \frac{1}{2} k (0.09)
\]

Now, we can compare the potential energies:

\[
PE_A = \frac{1}{2} k (0.36)
\]
\[
PE_B = \frac{1}{2} k (0.09)
\]

Since \( 0.36 > 0.09 \), it follows that:

\[
PE_A > PE_B
\]

Thus, Spring A has more potential energy than Spring B.

The correct answer is:

**A. Spring A has more potential energy than spring B.**