Energy and Work: Conservation of Energy and Work-Energy Theorem
Introduction
Energy and work are crucial concepts in physics. Energy is the capacity to do work, while work is the transfer of energy between systems. The conservation of energy states that energy cannot be created or destroyed but can be converted from one form to another. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
Key Concepts
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Energy: Energy is the ability to do work. It comes in many forms, such as potential, kinetic, thermal, electrical, or chemical energy. Energy is measured in joules (J).
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Work: Work is the transfer of energy from one system to another. Work is done when an object is moved by a force, and the displacement of the object is in the same direction as the force applied. Work is measured in joules (J).
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Conservation of Energy: The conservation of energy states that energy cannot be created or destroyed but can be converted from one form to another. The total amount of energy in a closed system remains constant. This principle is also known as the first law of thermodynamics.
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Work-Energy Theorem: The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In other words, the net work done on an object equals the change in its kinetic energy.
Equations and Formulas
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Energy: E=mc², where E is energy, m is mass, and c is the speed of light.
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Work: W=Fd, where W is work, F is force, and d is displacement.
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Kinetic Energy: KE=½mv², where KE is kinetic energy, m is mass, and v is velocity.
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Work-Energy Theorem: Wnet=ΔKE, where Wnet is the net work done, and ΔKE is the change in kinetic energy.
Examples
Example 1: A 2 kg object is dropped from a height of 10 m. What is the speed of the object just before it hits the ground?
Solution: The potential energy of the object at the initial position is (2 kg)(9.8 m/s²)(10 m)=196 J. When the object hits the ground, all of its potential energy is converted into kinetic energy. Therefore, the kinetic energy just before hitting the ground is 196 J. Using the formula KE=½mv², we can calculate the speed of the object as follows: v=√(2KE/m)=√(2×196/2)=√196=14 m/s.
Example 2: A car of mass 1500 kg is traveling at a constant velocity of 20 m/s. What is the net work done on the car in 10 seconds?
Solution: Since the car is traveling at a constant velocity, its kinetic energy does not change. Therefore, the net work done on the car is zero. We can calculate the work done by the engine to maintain the constant velocity using the formula W=Fd, where F is the force applied, d is the displacement, and W is the work done. Since the force applied is equal and opposite to the force of friction, the work done by the engine is equal and opposite to the work done by friction. Therefore, the net work done is zero.
References for Further Learning
- Physics Classroom. Work, Energy, and Power. https://www.physicsclassroom.com/class/energy/
- Khan Academy. Work and Energy. https://www.khanacademy.org/science/physics/work-and-energy
- MIT OpenCourseWare. Energy and Momentum. https://ocw.mit.edu/courses/physics/8-01sc-classical-mechanics-fall-2016/energy-and-momentum/
