Why Isn't Work Included in the Sum of Forces in Dynamics?

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SUMMARY

The discussion clarifies that work (W) is not included in the sum of forces in dynamics because it is not a force itself but rather a measure of energy transfer. The net force acting on a body is determined by the weight acting downward and the opposing forces from the springs, which together influence the body's acceleration. The relevant formula for the energy stored in a linear spring is ½.kx², which is essential for understanding the dynamics involved without needing calculus.

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Marchese_alex
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One question about this exercise. Why "W" isn't included in the sum of forces? Is doing work because is in the same direction of the movement, so I would assume that both the force of spring and weight would be in in my sum of forces. But this is not the case here, why is that?
 

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The weight of the body is partially opposed by the springs, but not fully. The resultant net force is downward and it accelerates the body downwards (but more slowly than if it were in free-fall). The force down is the weight, and the force up is that of two springs together with the inertial force (F = ma) of the body as it is accelerated.

You don't need to use calculus here if you memorize the formula that the energy stored in a linear spring is ½.kx² (and if you forget this formula you can work it out when needed like the author does here). :smile:
 
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