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Za Kh
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they say that a conservative force can be associated to a potential .. Why is that ? and what does it mean that a force has a potential ?
When we say the force field [itex] \vec F=F_x \hat x+F_y \hat y+F_z\hat z [/itex] has a potential, we mean that we can find a function like [itex] \Phi [/itex] such that [itex] F_x=-\frac{\partial \Phi}{\partial x} [/itex],[itex] F_y=-\frac{\partial \Phi}{\partial y} [/itex] and [itex] F_z=-\frac{\partial \Phi}{\partial z} [/itex]. It sometimes makes things easier because we can work with a scalar instead of a vector. Also it allows us to associate energy with forces so that we can apply conservation of energy.Za Kh said:Sry , but what does it mean that a force has a potential ?
Za Kh said:Sry , but what does it mean that a force has a potential ?
vanhees71 said:[itex]\vec \nabla \times \vec{g}=0 \quad , \quad \vec{\nabla} \cdot \vec{g}=-4 \pi \gamma \rho[/itex]
This implies that there's a gravitational potential [itex]\phi[/itex] such that
g⃗ =−∇⃗ ϕ
No, its not needed so don't bother. Its just mathematical details. I just wanted to get sure I'm standing on rock here!vanhees71 said:One can prove that the Helmholtz decomposition is unique up to a vectorial constant, if the vector field and its 1st derivatives vanishes at infinity. I don't know, where to find the formal proof of this. I'd have a look in textbooks on mathematical physics. If needed, I can try to find a reference.
A conservative force is a type of force that, when applied to a system, does not change the total mechanical energy of the system. This means that the work done by the force only depends on the initial and final positions of the system, and not on the path taken. Examples of conservative forces include gravity and elastic forces.
A conservative force is related to potential energy because the work done by a conservative force can be expressed as the change in potential energy. This is known as the work-energy theorem. As a system moves in a conservative force field, its potential energy changes, and this change is equal to the work done by the conservative force.
No, a conservative force cannot do positive work. This is because positive work implies that the force is adding energy to the system, which goes against the definition of a conservative force. A conservative force can only do negative work, which means it is taking energy away from the system and converting it into potential energy.
The main difference between conservative and non-conservative forces is that conservative forces do not change the mechanical energy of a system, while non-conservative forces do. Non-conservative forces, such as friction and air resistance, convert the mechanical energy of a system into other forms of energy, such as heat or sound.
The concept of conservative forces is used in physics to analyze the motion of objects in different systems. By identifying whether a force is conservative or not, we can determine the potential energy associated with the system and use it to calculate the work done by the force. This helps us understand and predict the behavior of objects in various situations.