Work–energy theorem

The major energy transformation in many situations is between forces doing work on a system and the kinetic energy of the system. The work–energy theorem states that the net work done on an object is always equal to its change in kinetic energy, as given in equation (10.2). Read the text aloud
(10.2) W net =Δ E k
Wnet  = net work done (J)
ΔEk  = change in kinetic energy (J)
Work–energy theorem
Equation (10.2) says that the net work done on a system equals the system’s change in kinetic energy. In this context, the word “net” means two things:
  1. The work is done by the net force, not by individual forces that may cancel or partially cancel each other; and
  2. the net work includes only the work done by the component of the net force that acts in the direction of the object’s motion.
The first requirement should be familiar since objects respond to the net force. When a net force does net work on an object, the object accelerates according to Newton’s second law and therefore gains kinetic energy. The second requirement is new and important. Other elements within a system may constrain the motion of an object so it does not move in the direction of the net force. An equivalent statement is that work is only done by the component of the net force in the direction of motion. Read the text aloud
The net work in equation (10.2) can be positive or negative. Consider a car on the road. A reaction force acts on the car created by the car’s engine applying a force against the road. The reaction force does positive work on the car, and the car’s kinetic energy increases. Work is positive when it is done on a system. Read the text aloud
Positive and negative work when driving a car
The car can also have its kinetic energy decreased by the driver applying the brakes. Brakes resist the rotation of the car’s wheels. This resistance creates a reaction force from the road that acts back against the car, opposite to the direction of motion. The quantity Fd is now negative and kinetic energy therefore decreases. In the context of the work–energy theorem, the net work can be positive or negative. When the net work is positive, the kinetic energy of the system increases. When the net work is negative, the kinetic energy of the system decreases. Read the text aloud
Sometimes forces do work that becomes stored potential energy. This happens when you stretch a rubber band. If that stretched rubber band is later used to launch a paper airplane, then the work done by the rubber band on the airplane is what increases the plane’s kinetic energy. Read the text aloud

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