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Work Energy Theorem

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Work Energy Theorem


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Learners calculate the amount of work done on an object and the energy transferred by the force acting on that object.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Describe that the change in an object’s kinetic energy is equal to the net work done on the object.
  • Describe work as the amount of energy transferred by force acting on an object for a given distance.
  • Explain that when a force and the work done by the force are in the same direction, positive work is done.
  • Explain that when a force and the work done by the force are in opposite directions, negative work is done.
  • Calculate the work done on or by a system.

Everything You'll Have Covered

The work-energy theorem states that the work done by the net force acting on a body will result in a net change in the body's kinetic energy. This is expressed as Conversely, if the kinetic energy of a body changes, it can be inferred that work has been done. Because kinetic energy is generally a function of velocity, knowing the initial and final velocity of a body of known mass allows us to use the formula K = mv2 to find ?K and thus calculate work. Work can be positive, resulting in an increase in kinetic energy, and therefore velocity, or negative, resulting in a decrease in kinetic energy and velocity.

Problems employing the work-energy theorem often involve an accelerating force. For example, if a force is applied to a car traveling at 20 m/s such that the car's velocity increases to 25 m/s, final kinetic energy will exceed the initial kinetic energy and positive work will have been done on the car. Given the mass of the vehicle as 2000 kg, work can be calculated as:

Further, because work is the result of a force applied over a distance (W = F?x), knowing one of the variables allows us to solve for the other. Problems can also involve the introduction of friction to a body in motion, such that the body slows or comes to a stop. Although the final kinetic energy may be zero, work will have been done because there was a net change. The theorem can also be applied to find an unknown force where there is no net change in kinetic energy.

The work-energy theorem is consistent with the law of conservation of mechanical energy; work is the means by which potential energy is transformed to kinetic energy and vice versa. Simple machines do not increase the amount of work done, but, by transferring a force applied over a longer distance to a shorter distance, they can increase the amount of force.

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Define the concept of work.Calculate the work done.Explain the conditions under which force can do work.Recognize types of energy.Define mechanical energy.Explain the energy lost by friction.
Course Physics
Type of Tutorial Problem Solving
Key Vocabulary conservation of energy, conservation of mechanical energy, distance