A body must do work against an opposing force to continue motion.
I have found this statement many times. But what is the reason behind it? Suppose $F_1$ is acting on a body to accelerate it (to increase its KE). Then another force $F_2$, less than the former, acts on the body in the opposite direction. So, according to the above statement, the body must have to lose energy.
But why will the body lose energy? Is it rather a rule or is there any logic? Now if $F_2$ becomes much greater than $F_1$, what will happen? Will the body still lose energy? Please give me logic so that I can understand this.
Answer
When two bodies interact, there is a force between them. Positive work is done on the object for which the dot product of force and velocity is positive. It follows that negative work is done on the object for which the dot product is negative.
By Newton's law (for each action there is an equal and opposite reaction), the force on one object is the reverse of the force on the other object - so necessarily if work done on one is positive, work done on the other is negative.
This is really just a statement of conservation of energy.
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