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07_ConservationOfEne.. - University of Colorado Boulder
07_ConservationOfEne.. - University of Colorado Boulder

... to change that PE into other kinds of energy (KE, thermal, light, etc ). The definition of the PE associated with a conservative force involves the work done by that force. Let’s first review the concept of work. Recall: If I lift a mass m, a distance h, at constant velocity (v = constant), with an ...
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... field. We measured its radius with a meter stick at r = 20.4 ± .1 cm. A variable high-voltage power supply determined the strength of the magnetic field inside the sphere. The magnitude of this field was measured with a gaussmeter, which worked by measuring the Hall Effect across a metal probe insid ...
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... velocity. Then you can write the numerator of the equation above as follows: mΔv = m (v f − vi ) = mv f − mvi mΔv = p f − pi mΔv = Δp In this equation, the ball’s initial momentum is pi (= mvi) and the final momentum is pf (= mvf). Therefore, the equation for Newton’s second law can be written as th ...
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Classical central-force problem



In classical mechanics, the central-force problem is to determine the motion of a particle under the influence of a single central force. A central force is a force that points from the particle directly towards (or directly away from) a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center. In many important cases, the problem can be solved analytically, i.e., in terms of well-studied functions such as trigonometric functions.The solution of this problem is important to classical physics, since many naturally occurring forces are central. Examples include gravity and electromagnetism as described by Newton's law of universal gravitation and Coulomb's law, respectively. The problem is also important because some more complicated problems in classical physics (such as the two-body problem with forces along the line connecting the two bodies) can be reduced to a central-force problem. Finally, the solution to the central-force problem often makes a good initial approximation of the true motion, as in calculating the motion of the planets in the Solar System.
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