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Hertz's principle of least curvature is a special case of Gauss's principle, restricted by the three conditions that there are no externally applied forces, no interactions (which can usually be expressed as a potential energy), and all masses are equal. Without loss of generality, the masses may be set equal to one.
This is an application of the minimum energy principle. Alternatively, suppose we have a cylinder containing an ideal gas, with cross sectional area A and a variable height x. Suppose that a weight of mass m has been placed on top of the cylinder. It presses down on the top of the cylinder with a force of mg where g is the acceleration due to ...
Mass–energy equivalence states that all objects having mass, or massive objects, have a corresponding intrinsic energy, even when they are stationary.In the rest frame of an object, where by definition it is motionless and so has no momentum, the mass and energy are equal or they differ only by a constant factor, the speed of light squared (c 2).
For two pairwise interacting point particles, the gravitational potential energy is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): = = where is the displacement vector of the mass, is gravitational force acting on it and denotes scalar product.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
Internal forces between the particles that make up a body do not contribute to changing the momentum of the body as there is an equal and opposite force resulting in no net effect. [ 3 ] The linear momentum of a rigid body is the product of the mass of the body and the velocity of its center of mass v cm .
In scientific contexts, mass is the amount of "matter" in an object (though "matter" may be difficult to define), but weight is the force exerted on an object's matter by gravity. [1] At the Earth 's surface, an object whose mass is exactly one kilogram weighs approximately 9.81 newtons , the product of its mass and the gravitational field ...
The slug is defined as the amount of mass that accelerates at 1 ft/s 2 when one pound-force is exerted on it, and is equivalent to about 32.2 pounds (mass). The kilogram-force is a non-SI unit of force, defined as the force exerted by a one-kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly).