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1、AP Physics C Mechanics Review Sheet #4-Newtons Law of Universal Gravitation The gravitational force between two objects is directly related to the product of the masses of the objects and inversely related to the distance between their center of masses squared When an object is located inside the su
2、rface of the larger object, only the mass beneath the object being affected applies a force. One must use the assumption that the planet is of uniform density, so that the large M in the equation is replaced by, where rho is the density.The force of gravity equation is then:-Gravitational Potential
3、Energy At infinity, the gravitational potential energy that an object experiences is zero, and as it gets closer to the source, the potential energy must decrease. So, the gravitational potential energy should be negative-Circular Orbits For objects traveling in circular orbits, e.g., satellites, on
4、e should set the force of gravity equal to the centripetal force acting upon the object to determine its orbital velocity Total Energy in a circular orbit is equal to the sum of the kinetic and the gravitational potential, and reduces to a relationship Keplers Third Law () can be derived from settin
5、g centripetal force equal to gravitational force-Elliptical Orbits The main difference is that you cannot set centripetal force equal to gravitational force Keplers 1st Law- Planets move in elliptical orbits with the Sun at one focus Keplers 2nd Law- Planets move faster closer to the sun Keplers 3rd
6、 Law- The period squared is proportional to the semi-major axis cubed Total Energy in the system is, again, the sum of the kinetic and the gravitational potential, but because you cannot solve for the velocity, there is nothing it reduces down to-Escape Velocity The minimum required velocity for an
7、object to leave a planet and stop only when reaching infinityOscillations & SHM-Simple Harmonic Motion Defined as an object oscillating around a given equilibrium point, where the maximum force applied is at the maximum displacement and the maximum velocity occurs at the equilibrium point Motion fol
8、lows either a sinusoidal or cosinusoidal curve is the angular frequency, and equals , where T is the period The velocity and acceleration functions can be found by taking the derivative of the position function The general form of the acceleration must be for the object to be following SHM-Energy in
9、 SHM The total amount of energy in the system is equal to the potential energy at the maximum displacement, which is equal to the kinetic energy at the equilibrium point-Pendula The pendulum in which the string is considered to have negligible mass is called a simple pendulum The equation for the pe
10、riod of a simple pendulum is This equation only holds true for small amplitudes, where the sine of the angle is nearly equal to the angle itself in radians-Mass on a Spring Mass on a spring systems also move according to simple harmonic motion The equation for the period of a mass-spring system is W
11、hen a mass-spring system is vertical, the mass will oscillate around the equilibrium point, which can be determined by setting the force of the spring equal to the force of gravitywhere x is the stretched distance of the spring At the maximum amplitude, the total energy in the mass-spring system can be determined by integrating the force equation with respect to distance to get, for an ideal spring, When one attempts to determine the maximum velocity at the equilibrium position, one should set the spring potential energy equation equal to the kinetic energy relationship to determine the speed
