Does work=potential energy?  Please explain the formula work= negative potential energy.  Does this mean negative work=positive potential energy?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Work and energy are both expressed in terms of the SI unit: Joule, (J).

When work is done on a body, a force is applied on it. This either makes the body accelerate at a rate that is inversely proportional to its mass and directly proportional to the force applied. Else the work leads to an increase in the potential energy.

For example, if a force were applied to a body in the horizontal direction, it would accelerate. On the other hand if the force were applied vertically in the upward direction and the resulting acceleration were greater than that due to gravity, the body would rise up. The work done is partially stored in the form of gravitational potential energy.

The work done leads to an increase in the potential energy. Negative potential energy means a decrease in the potential energy. This decrease results in work which ultimately accelerates the body over a certain distance. A body that is falling downwards loses potential energy, and accelerates downwards.

Negative work is the work done against an opposing force. This may result in an increase in potential energy. Consider again the example provided earlier, when we apply a force on the body against the gravitational force of attraction it is negative in terms of the gravitational force. This also results in an increase in the gravitational potential energy.

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