Understanding the Basics of Elastic Potential Energy

Oct 13, 2025 by thesweetdesigns.com 43 views

Understanding the Basics of Elastic Potential Energy

Elastic potential energy is a form of potential energy that is stored in an object due to its deformation. When a rubber band is stretched or compressed, it stores energy in the form of elastic potential energy. This energy is directly proportional to the spring constant of the rubber band and the square of the displacement from its equilibrium position.

The Formula for Elastic Potential Energy

The formula for elastic potential energy is given by:

U = \frac{1}{2}kx^2

where:

$U$ is the elastic potential energy
$k$ is the spring constant
$x$ is the displacement from the equilibrium position

Given Values

In this problem, we are given the following values:

$U = 5 \, \text{J}$ (elastic potential energy)
$k = 50 \, \text{N/m}$ (spring constant)

Calculating Displacement

We can use the formula for elastic potential energy to calculate the displacement of the rubber band. Rearranging the formula to solve for $x$ , we get:

x = \sqrt{\frac{2U}{k}}

Substituting the given values, we get:

x = \sqrt{\frac{2(5 \, \text{J})}{50 \, \text{N/m}}}

Simplifying the expression, we get:

x = \sqrt{\frac{10 \, \text{J}}{50 \, \text{N/m}}}

x = \sqrt{0.2 \, \text{m}^2}

x = 0.447 \, \text{m}

Rounding to the Nearest Answer Choice

Rounding the calculated value to the nearest answer choice, we get:

x \approx 0.4 \, \text{m}

Conclusion

In conclusion, the displacement of the rubber band is approximately $0.4 \, \text{m}$ .

Answer Choice

The correct answer choice is:

C. 0.4 m

Additional Information

It's worth noting that the calculated value of $0.447 \, \text{m}$ is not among the answer choices. However, rounding to the nearest answer choice, we get $0.4 \, \text{m}$ , which is the closest answer choice.

References

[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). John Wiley & Sons.
[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage Learning.

Discussion

Q: What is elastic potential energy?

A: Elastic potential energy is a form of potential energy that is stored in an object due to its deformation. When a rubber band is stretched or compressed, it stores energy in the form of elastic potential energy.

Q: What is the formula for elastic potential energy?

A: The formula for elastic potential energy is given by:

U = \frac{1}{2}kx^2

where:

$U$ is the elastic potential energy
$k$ is the spring constant
$x$ is the displacement from the equilibrium position

Q: How do I calculate the displacement of a rubber band?

A: To calculate the displacement of a rubber band, you can use the formula for elastic potential energy and rearrange it to solve for $x$ . The formula becomes:

x = \sqrt{\frac{2U}{k}}

Q: What is the spring constant, and how is it related to the displacement of a rubber band?

A: The spring constant is a measure of the stiffness of a rubber band. It is defined as the force required to displace the rubber band by a unit distance. The spring constant is directly proportional to the displacement of the rubber band, as shown in the formula for elastic potential energy.

Q: Can I use the formula for elastic potential energy to calculate the energy stored in a rubber band?

A: Yes, you can use the formula for elastic potential energy to calculate the energy stored in a rubber band. Simply rearrange the formula to solve for $U$ , and use the given values for $k$ and $x$ .

Q: What are some real-world applications of elastic potential energy?

A: Elastic potential energy has many real-world applications, including:

Springs and shock absorbers in vehicles
Rubber bands and elastic strings in musical instruments
Elastic fibers in clothing and textiles
Energy storage in batteries and capacitors

Q: Can I use the formula for elastic potential energy to calculate the displacement of a spring?

A: Yes, you can use the formula for elastic potential energy to calculate the displacement of a spring. The formula is the same as for a rubber band, and the only difference is that the spring constant is typically given in units of N/m.

Q: What is the difference between elastic potential energy and kinetic energy?

A: Elastic potential energy is the energy stored in an object due to its deformation, while kinetic energy is the energy of motion. When a rubber band is stretched or compressed, it stores energy in the form of elastic potential energy. When it is released, the energy is converted to kinetic energy.

Q: Can I use the formula for elastic potential energy to calculate the energy stored in a stretched or compressed object?

A: Yes, you can use the formula for elastic potential energy to calculate the energy stored in a stretched or compressed object. The formula is the same as for a rubber band, and the only difference is that the object may have a different spring constant and displacement.

Q: What are some common mistakes to avoid when using the formula for elastic potential energy?

A: Some common mistakes to avoid when using the formula for elastic potential energy include:

Using the wrong units for the spring constant and displacement
Failing to account for the direction of the force and displacement
Using the formula for kinetic energy instead of elastic potential energy
Failing to consider the effects of friction and other external forces.