Summary of Work: Elastic Force

Goals

1. Grasp that the work done by an elastic force stems from Hooke's Law.

2. Calculate the work of the elastic force using the formula W = kx²/2.

3. Connect the concepts of elastic force and work to real-world job applications.

4. Develop practical skills in working with elastic materials.

Contextualization

Throughout history, our understanding of forces and motion has enabled incredible achievements. A prime example is the use of bows and arrows, where elastic force is vital to how the bow functions. The energy stored in the bowstring, when drawn back, transforms into work that sends the arrow flying, which was crucial for hunting and warfare in ancient times. Today, elastic force remains essential, from the design of springs in our vehicles to building structures that can withstand earthquakes.

Subject Relevance

To Remember!

Hooke's Law

Hooke's Law states that the force needed to stretch or compress a spring is directly proportional to how much the spring is stretched or compressed. In mathematical terms, it’s expressed as F = -kx, where F represents the applied force, k is the spring's elastic constant, and x is how much the spring is deformed.

• The elastic constant (k) varies based on the material and structure of the spring.

• The elastic force is a restoring force that always acts in the opposite direction of the deformation.

• Hooke's Law only applies to elastic deformations, where the spring returns to its original shape after the force is removed.

Elastic Force

The elastic force is the force that an elastic material—like a spring or rubber band—exerts to revert back to its original shape after being deformed. This force relates directly to the deformation experienced by the material, as outlined by Hooke's Law.

• The elastic force is a conservative force, meaning that the work it does is dependent only on the starting and ending points of deformation.

• It can either compress or stretch the material, depending on how it is being manipulated.

• This principle serves as the basis for many devices, such as car shocks and spring scales.

Work Done by an Elastic Force

The work done by an elastic force represents the energy transferred to an object by that force during displacement. This is calculated using the formula W = kx²/2, where W stands for work, k is the elastic constant, and x is the deformation of the material.

• The work conducted by an elastic force can be either positive or negative, depending on the deformation's direction in relation to the applied force.

• This stored energy can be released later, as seen in trampolines or bows.

• The W = kx²/2 formula is derived from integrating the elastic force over the deformation.

Practical Applications

• In automotive engineering, springs are vital in suspension systems to absorb shocks for a smoother ride.

• In civil engineering, elastic materials are utilized to create structures that can absorb and dissipate energy from earthquakes, making buildings more resilient.

• In product design, Hooke's Law is applied to craft ergonomic and durable items, such as toys, sports gear, and medical devices.

Key Terms

• Hooke's Law: The principle that defines the linear relationship between the force applied to an elastic material and the resulting deformation.

• Elastic Force: The restoring force that an elastic material applies to return to its original shape after deformation.

• Work: The energy transferred to an object by a force acting over a distance, in the case of elastic force calculated using the formula W = kx²/2.

• Elastic Constant (k): A parameter that defines the stiffness of an elastic material, indicating how much force is needed to deform it by a unit length.

Questions for Reflections

• How can understanding elastic force and Hooke's Law influence the creation of new products and technologies?

• What challenges and limitations arise in applying Hooke's Law in real-world scenarios, such as building earthquake-resistant structures?

• In what ways could knowing how to calculate the work done by an elastic force benefit various careers?

Practical Challenge: Building an Elastic Force Meter

This mini-challenge is designed to reinforce understanding of Hooke's Law and elastic force by constructing a simple measuring device.

Instructions

• Form groups of 3-4 people.

• Gather materials: rubber bands, a ruler, small weights (like coins), paper, and a pen for notes.

• Secure one rubber band at one end of the ruler.

• Attach a weight at the other end of the rubber band and measure the rubber band’s extension using the ruler.

• Record both the initial extension and the final extension of the rubber band.

• Repeat the experiment by adding more weights and document the new extensions.

• Calculate the elastic constant (k) of the rubber band based on your measurements.

• Use the formula W = kx²/2 to find the work done by the elastic force for each measurement.