Learning Outcomes
i. Recognize the applicability of the work-energy theorem in a resistive medium, where non-conservative forces like friction act.
ii. Comprehend the modifications required to apply the work-energy theorem in the presence of resistive forces.
iii. Apply the work-energy theorem to calculate the change in kinetic energy of an object moving in a resistive medium.
iv. Analyze the energy transformations involved in motion through a resistive medium, including the dissipation of energy into heat.
v. Solve problems involving motion in resistive media using the work-energy theorem.
Introduction
In our previous lessons, we delved into the concept of the work-energy theorem, a fundamental principle governing energy transformations in various physical systems. However, our focus was primarily on conservative systems, where only conservative forces act. In this lesson, we venture into a more complex realm: the work-energy theorem in a resistive medium, where non-conservative forces, such as friction, play a significant role.
i. The Work-Energy Theorem in Resistive Medium: Adapting to Opposing Forces
The work-energy theorem, in its original form, states that the net work done on an object equals its change in kinetic energy. However, when resistive forces are present, the net work done on the object is not solely responsible for its change in kinetic energy. A portion of the work done is dissipated into other forms, such as heat, due to the action of resistive forces.
ii. Modifications to the Work-Energy Theorem: Accounting for Energy Dissipation
To account for energy dissipation in resistive media, we modify the work-energy theorem by introducing the concept of work done by non-conservative forces. The modified work-energy theorem states that the total work done on an object equals the change in its kinetic energy plus the work done by non-conservative forces.
iii. Applying the Work-Energy Theorem in Resistive Media: Solving for Kinetic Energy Changes
To apply the work-energy theorem in a resistive medium, we follow these steps:
- Identify all the forces acting on the object, including both conservative and non-conservative forces.
- Calculate the net work done on the object by considering the contributions from both conservative and non-conservative forces.
- Determine the work done by non-conservative forces using appropriate formulas or problem-specific information.
- Apply the modified work-energy theorem to calculate the change in kinetic energy of the object.
iv. Energy Transformations in Resistive Media: From Motion to Heat
In a resistive medium, the work done by non-conservative forces is not directly converted into kinetic energy. Instead, it is dissipated as heat due to the frictional interactions between the object and the medium. This energy dissipation explains why objects eventually slow down and come to rest when moving in a resistive medium.
v. Solving Problems Using the Work-Energy Theorem: A Practical Application
The work-energy theorem is a powerful tool for analyzing motion in resistive media. By applying the modified work-energy theorem, we can calculate the change in kinetic energy of an object moving in a resistive medium and gain insights into the energy transformations involved.
The work-energy theorem in a resistive medium provides a comprehensive framework for understanding energy transformations in physical systems where non-conservative forces act. By recognizing the modifications required to account for energy dissipation and applying the modified work-energy theorem, we can analyze motion and energy changes in a variety of scenarios involving resistive media. This knowledge empowers us to solve problems, understand the limitations of mechanical systems, and appreciate the intricate interplay between energy and motion in our physical world.
