I'm trying to solve a task using energy conservation laws. An object with a known coefficient of kinetic friction is propelled by the magnetic field horizontally. We can calculate the loss of energy by the kinetic friction using the $A=Fd$ formula describing work done by the force of kinetic friction since we also know how far it moved and its mass. Yet I struggle with calculating how much energy would be wasted in order to overcome the force of static friction. The body doesn't move throughout the process, so work will be equal to zero? Is there a separate method for this?
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Yet I struggle with calculating how much energy would be wasted in order to overcome the force of static friction.
It requires a force that exceeds the maximum possible static friction force in order to overcome static friction on an object. Up until that force is reached, the applied force does no work because it causes no displacement of the object.
However, in the case of say a person supplying the force, that person may expend energy "internally" applying that force, even though the person does not perform any physics work. The person's work is "physiological" . Richard Feynman in his physics lectures explains it the following way: (note: he talks about holding a weight without moving it. The same would apply to trying to push something against static friction without moving it):
The fact that we have to generate effort to hold up a weight is simply due to to the design of striated muscle. What happens is when a nerve impulse reaches a muscle fiber, the fiber gives a little twitch and then relaxes, so that when we hold something up , enormous volleys of nerve impulses are coming in to the muscle, large numbers of twitches are maintaining the weight, while other fibers relax. When we hold a heavy weight we get tired, begin to shake, ...because the muscle is tired and not reacting fast enough.
However, I would not say the energy the person expended is "wasted". Although technically not performing any work, the energy expended did generate the necessary force to overcome static friction.
Hope this helps.
