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The forces acting on a body add as vectors, and so the total force on a body depends upon both the magnitudes and the directions of the individual forces. [23]: 58 When the net force on a body is equal to zero, then by Newton's second law, the body does not accelerate, and it is said to be in mechanical equilibrium.
In this scenario, the gravitational force is mostly, but not entirely, diminished; anyone in the elevator would experience an absence of the usual gravitational pull, however the force is not exactly zero. Since gravity is a force directed towards the center of the Earth, two balls a horizontal distance apart would be pulled in slightly ...
Consider a body Q of volume V with density ρ(r) at each point r in the volume. In a parallel gravity field the force f at each point r is given by, = ^ = ^, where dm is the mass at the point r, g is the acceleration of gravity, and ^ is a unit vector defining the vertical direction.
In addition to gravity, the shell theorem can also be used to describe the electric field generated by a static spherically symmetric charge density, or similarly for any other phenomenon that follows an inverse square law. The derivations below focus on gravity, but the results can easily be generalized to the electrostatic force.
For points inside a spherically symmetric distribution of matter, Newton's shell theorem can be used to find the gravitational force. The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point located a distance r 0 from the center of the mass distribution: [13]
The gravitational potential (V) at a location is the gravitational potential energy (U) at that location per unit mass: =, where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
The important point of this is that the zero-point field energy H F does not affect the Heisenberg equation for a kλ since it is a c-number or constant (i.e. an ordinary number rather than an operator) and commutes with a kλ. We can therefore drop the zero-point field energy from the Hamiltonian, as is usually done.
When a force acts on a particle, it is applied to a single point (the particle volume is negligible): this is a point force and the particle is its application point. But an external force on an extended body (object) can be applied to a number of its constituent particles, i.e. can be "spread" over some volume or surface of the body.