How Is Work Done By External Force Equal To Change In Total Mechanical Energy?
Introduction
In physics, the concept of work and energy is a fundamental aspect of understanding the behavior of objects in various situations. When an external force is applied to an object, it can cause a change in the object's kinetic energy, potential energy, or both. In this article, we will explore how the work done by an external force is equal to the change in total mechanical energy of an object.
Understanding Work and Energy
Before we dive into the details, let's first understand the concepts of work and energy. Work is defined as the product of the force applied to an object and the distance over which the force is applied, in the direction of the force. Mathematically, work (W) is represented as:
W = F × d × cos(θ)
where F is the force applied, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion.
Energy, on the other hand, is the ability of an object to do work. There are two types of energy: kinetic energy (KE) and potential energy (PE). Kinetic energy is the energy of motion, while potential energy is the energy an object possesses due to its position or configuration.
Work Done by External Forces
When an external force is applied to an object, it can cause a change in the object's kinetic energy, potential energy, or both. The work done by an external force is equal to the change in total mechanical energy of the object. Mathematically, this can be represented as:
Wext = ΔKE + ΔPE
where Wext is the work done by the external force, ΔKE is the change in kinetic energy, and ΔPE is the change in potential energy.
Work Done by Internal Forces
Internal forces, such as friction, are forces that act within an object or between objects. These forces do not change the total mechanical energy of an object, but rather convert some of the object's energy into heat or other forms of energy. The work done by internal forces is represented as:
Wint = 0
Example: A Ball Rolling Down a Hill
Consider a ball rolling down a hill. As the ball rolls, it gains kinetic energy due to the force of gravity acting on it. The work done by gravity is equal to the change in the ball's kinetic energy and potential energy. Mathematically, this can be represented as:
Wext = ΔKE + ΔPE
where Wext is the work done by gravity, ΔKE is the change in kinetic energy, and ΔPE is the change in potential energy.
Conservative and Non-Conservative Forces
Forces can be classified into two categories: conservative and non-conservative. Conservative forces, such as gravity, always act in the direction of the force and do not depend on the path taken by the object. Non-conservative forces, such as friction, act in the direction of the force but depend on the path taken by the object.
Work Done by Non-Conservative Forces
Non-conservative forces, such as friction, do not change the total mechanical energy of an object. However, they can cause a change in the object's kinetic energy and potential energy. Mathematically, this can be represented as:
Wext = ΔKE + ΔPE
where Wext is the work done by the non-conservative force, ΔKE is the change in kinetic energy, and ΔPE is the change in potential energy.
Conclusion
In conclusion, the work done by an external force is equal to the change in total mechanical energy of an object. This is a fundamental principle of physics that helps us understand the behavior of objects in various situations. By understanding the concepts of work and energy, we can better appreciate the complex interactions between objects and the forces that act upon them.
References
- [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
- [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
- [3] Young, H. D., & Freedman, R. A. (2015). University physics. Addison-Wesley.
Additional Resources
- [1] Khan Academy. (n.d.). Work and energy. Retrieved from https://www.khanacademy.org/science/physics/work-and-energy
- [2] Physics Classroom. (n.d.). Work and energy. Retrieved from https://www.physicsclassroom.com/class/momentum/Lesson-1/Work-and-Energy
FAQs
- Q: What is work in physics? A: Work is the product of the force applied to an object and the distance over which the force is applied, in the direction of the force.
- Q: What is energy in physics? A: Energy is the ability of an object to do work.
- Q: What is the difference between conservative and non-conservative forces?
A: Conservative forces, such as gravity, always act in the direction of the force and do not depend on the path taken by the object. Non-conservative forces, such as friction, act in the direction of the force but depend on the path taken by the object.
Work and Energy Q&A =====================
Q: What is work in physics?
A: Work is the product of the force applied to an object and the distance over which the force is applied, in the direction of the force. Mathematically, work (W) is represented as:
W = F × d × cos(θ)
where F is the force applied, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion.
Q: What is energy in physics?
A: Energy is the ability of an object to do work. There are two types of energy: kinetic energy (KE) and potential energy (PE). Kinetic energy is the energy of motion, while potential energy is the energy an object possesses due to its position or configuration.
Q: What is the difference between conservative and non-conservative forces?
A: Conservative forces, such as gravity, always act in the direction of the force and do not depend on the path taken by the object. Non-conservative forces, such as friction, act in the direction of the force but depend on the path taken by the object.
Q: What is the work-energy theorem?
A: The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Mathematically, this can be represented as:
Wnet = ΔKE
where Wnet is the net work done on the object, and ΔKE is the change in its kinetic energy.
Q: What is the difference between work and energy?
A: Work is the transfer of energy from one object to another through a force applied over a distance. Energy, on the other hand, is the ability of an object to do work.
Q: Can work be negative?
A: Yes, work can be negative. If the force applied to an object is opposite to the direction of motion, the work done is negative.
Q: Can energy be negative?
A: No, energy cannot be negative. Energy is a scalar quantity and always has a positive value.
Q: What is the unit of work?
A: The unit of work is the joule (J). One joule is equal to one newton-meter (N·m).
Q: What is the unit of energy?
A: The unit of energy is also the joule (J). One joule is equal to one newton-meter (N·m).
Q: Can work be done by a force that is not applied to an object?
A: No, work can only be done by a force that is applied to an object. If a force is not applied to an object, no work is done.
Q: Can energy be transferred from one object to another without work being done?
A: Yes, energy can be transferred from one object to another without work being done. For example, when a hot cup of coffee is placed on a table, the energy from the coffee is transferred to the table, but no work is done.
Q: What is the difference between internal and external forces?
A: Internal forces, such as friction, are forces that act within an object or between objects. External forces, such as gravity, are forces that act on an object from outside.
Q: Can internal forces do work?
A: Yes, internal forces can do work. For example, when a car's engine is running, the internal forces within the engine do work to propel the car forward.
Q: Can external forces do work?
A: Yes, external forces can do work. For example, when a person pushes a box, the external force of the person's hand does work to move the box.
Q: What is the relationship between work and energy?
A: The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Mathematically, this can be represented as:
Wnet = ΔKE
where Wnet is the net work done on the object, and ΔKE is the change in its kinetic energy.
Q: Can work be converted into other forms of energy?
A: Yes, work can be converted into other forms of energy. For example, when a car's engine is running, the work done by the engine is converted into kinetic energy, which propels the car forward.
Q: Can energy be converted into work?
A: Yes, energy can be converted into work. For example, when a person lifts a heavy object, the energy stored in their muscles is converted into work to lift the object.
Q: What is the difference between potential and kinetic energy?
A: Potential energy is the energy an object possesses due to its position or configuration. Kinetic energy is the energy of motion.
Q: Can potential energy be converted into kinetic energy?
A: Yes, potential energy can be converted into kinetic energy. For example, when a ball is rolled down a hill, the potential energy of the ball is converted into kinetic energy.
Q: Can kinetic energy be converted into potential energy?
A: Yes, kinetic energy can be converted into potential energy. For example, when a ball is thrown upwards, the kinetic energy of the ball is converted into potential energy.
Q: What is the relationship between potential and kinetic energy?
A: The total mechanical energy of an object is the sum of its potential energy and kinetic energy. Mathematically, this can be represented as:
E = PE + KE
where E is the total mechanical energy, PE is the potential energy, and KE is the kinetic energy.