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kgm2s-2
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We all know that the definition for work is
W = ∫F.ds
Why can't it be
W = ∫s.dF?
W = ∫F.ds
Why can't it be
W = ∫s.dF?
kgm2s-2 said:We all know that the definition for work is
W = ∫F.ds
Why can't it be
W = ∫s.dF?
Yes, actually that's what it would mean if you did the integration by parts thing.chrisbaird said:Do you see the problem? What is s(F_{1}) supposed to mean physically? The displacement applied at the certain force strength F_{1}?
I don't see how the cause-and-effect relationship is relevant. And in any case, it is often possible to view displacements as causing forces. For example, if I have a mass on a spring and I displace it, that causes a different force to exist.chrisbaird said:This doesn't mean anything. Forces causes displacements to do work. Displacements don't cause the forces.
kgm2s-2 said:Why can't it be
W = ∫s.dF?
But [itex]W=Fx-\int x dF[/itex] (derived using integration by parts, evaluated at the beginning and end of the displacement) doesn't have this problem.AlephZero said:That definition would mean that if F was constant, dF would be 0 and W would be 0 for any value of s.
That doesn't answer the OP's question. The OP wants to know *why* work is defined a certain way.AlephZero said:That isn't how "mechanical work" is defined.
kgm2s-2 said:It seems like it is because ∫s.dF doesn't have a physical meaning so we can't use it to find work done?
So for a force vs displacement graph, ∫F.ds is talking about the area under the curve and the x-axis while ∫s.dF is talking about the area bounded by the curve and the y-axis. Hence ∫s.dF does not have a physical meaning?
∫s.dF is talking about the area bounded by the curve and the y-axis. Hence ∫s.dF does not have a physical meaning?
The definition for mechanical work is the amount of force applied to an object over a distance to cause a displacement. It is a form of energy transfer that results in a change in the position or motion of an object.
The formula for calculating mechanical work is W = F * d, where W is work, F is force, and d is distance.
The units of measurement for mechanical work are joules (J) in the metric system and foot-pounds (ft-lb) in the imperial system.
Work is the amount of energy transferred to an object, while power is the rate at which work is done. In other words, work is a measure of the total energy used, while power is a measure of how quickly that energy is used.
Mechanical work is a form of energy transfer, meaning it is a way in which energy can be moved from one object to another. The work done on an object increases its energy, while the work done by an object decreases its energy.