Ch01 Newtonian mechanics

12 can be inserted in the energy equation eq 13 and

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Unformatted text preview: kinetic, Eq. (1.2) can be inserted in the energy equation, Eq. (1.3), and one obtains with (d2 / dt2) x = v(d / dx) v E kin = 1 m v2 2 = p2 . 2m (1.5) If no external forces act on the particle, then the total energy of the particle is a constant and is the sum of potential and kinetic energy E total = E kin + U ( x) = p2 + U ( x) . 2m (1.6) An example of a one-dimensional potential function is shown in Fig. 1.1. Consider a classical object, e. g. a soccer ball, positioned on one of the two slopes of the potential, as shown in Fig. 1.1. Once the ball is released, it will move downhill with increasing velocity, reach the maximum velocity at the bottom, and move up on the opposite slope until it comes to a momentary complete stop at the classical turning point. At the turning point, the energy of the ball is purely potential. The ball then reverses its direction of motion and will move again downhill. In the absence of friction, the ball will continue forever to oscillate between the two classical turning points...
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