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Work-energy Theorem

### 7.8: Work-energy Theorem

According to Newton’s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the momentum of the particle (motion). Therefore, we should consider the work done by all forces acting on a particle, or the net work, to see its effect on the particle’s motion.

The work-energy theorem equates work done by all the forces on an object to the change in its kinetic energy. The theorem can be used to calculate work done by a force when acceleration is not constant, provided we know the change in velocity. When approaching a problem using the work-energy theorem, the following steps should be considered.

1. Identify the given quantities and draw a free-body diagram based on the forces acting on the object. Calculate the work done by the known forces, keeping the sign of work done in mind. Add the total amount of work done by each force.
2. Use the work-energy theorem and equate the total work to the change in kinetic energy. Substitute the known quantities and solve for the unknown.
3. Evaluate the answer. If the object is traveling at a constant speed, there is no change in kinetic energy; therefore, the total work done should be zero. If the object has accelerated or has increased kinetic energy, the total work done is positive. If the object has slowed down, the total work done is negative.

This text is adapted from Openstax, University Physics Volume 1, Section 7.3: Work-Energy Theorem.

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