Question

Show that a central force as a negative gradient of potential energy

Answer 1

Answer:

The force exerted by the force field always tends toward lower energy and will act to reduce the potential energy. The negative sign on the derivative shows that if the potential U increases with increasing r, the force will tend to move it toward smaller r to decrease the potential energy.

Answer 2

Show that a central force as a negative gradient of potential energy

• Since the angle of any field (like the gravitational possible field) focuses toward the biggest expansion in that field. Envision going on a climb. The slope will point in whichever course is the steepest uphill.

• Yet, things roll downhill, going to bring down expected energies. That is accomplished by a power (for this situation, the part of the gravitational power along the surface). The power will point toward the biggest abatement in potential (energy) - in the negative of the slope of the possible field.

• Assuming you move an item in a gravitational field from A to B against the power of gravity thus moving energy to the item, then, at that point, we can record the energy moved to the article in two ways.

energy moved = power x distance = F Δ(- X)

energy moved = change in possible energy =  Δ(GPE)

Presently we compare postulations two articulations F Δ(- X) = Δ (GPE)

revamp: F= - Δ(GPE)/Δ (X) and 'Δ(GPE)/Δ (X)' is the potential energy angle.