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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.

bobie
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3 Answers3

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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.

Floris
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If multiple forces act on a body at the same time, you should compute the net force before considering whether it is increasing or decreasing the kinetic energy of the object, and thus whether the work done by the force is positive or negative.

So, using your example, the net force is $F = F_1 + F_2$, and since $F_1 > 0$, $F_2 < 0$ and $|F_2|< F_1$ then $0 < F < F_1 $ and so, if the object is moving along the positive axis and $\Delta x > 0$, the work $W = F \cdot \Delta x$ done is positive.

Now, if the two forces don't act simultaneously then the work will first be positive, as both $\Delta x > 0$ and $F > 0$, then negative, since now $\Delta x > 0$ but $F < 0$.

Jessica Hansen
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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?

The logic you are looking for is not third law, it is called negative work

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and the formula is

From the definition of the dot product, we have $$ W = F\Delta x\cos\theta $$ Where $F$ is the magnitude of $\mathbf F$, $\Delta x$ is the magnitude of $\Delta \mathbf x$, and $\theta$ is the angle between $\mathbf F$ and $\Delta\mathbf x$. Note, in particular that the magnitudes are positive by definition, so the $\cos\theta$ is negative if and only of $\theta$ is between $90^\circ$ and $180^\circ$. ... and the component opposite the motion contributes a negative amount to the work.

Therefore, if the angle is 180°, we have: $$ W = > F* d * -1 = (\cos 180°) $$ When we lift a box with an upward force F > g , g does negative work W -10m N on the box, and the net force is the difference F - W, according to vector addition