# SUMMARY

Newton’s law of gravitation: Any two particles with masses m1 and m2, a distance r apart, attract each other with forces inversely proportional to r2 . These forces form an action–reaction pair and obey Newton’s third law. When two or more bodies exert gravitational forces on a particular body, the total gravitational force on that individual body is the vector sum of the forces exerted by the other bodies. The gravitational interaction between spherical mass distributions, such as planets or stars, is the same as if all the mass of each distribution were concentrated at the center.

Topics You May Be Interested In
Standards And Units Kepler's Second Law
Finding And Using The Center Of Gravity A Point Mass Outside A Spherical Shell
Summary Of Equilibrium And Elasticity Black Holes
Fluid Mechanics Describing Oscillation
Weight Simple Harmonic Motion

Topics You May Be Interested In
Solving Physics Problems Solved Problems
Uncertainty And Significant Figures Weight
Elasticity And Plasticity Gravitational Potential Energy
Pressure, Depth, And Pascals Law More On Gravitational Potential Energy
Deriving Bernoullis Equation Spherical Mass Distributions

Gravitational force, weight, and gravitational potential energy: The weight w of a body is the total gravitational force exerted on it by all other bodies in the universe. Near the surface of the earth (mass mE and radius RE), the weight is essentially equal to the gravitational force of the earth alone. The gravitational potential energy U of two masses m and mE separated by a distance r is inversely proportional to r. The potential energy is never positive; it is zero only when the two bodies are infinitely far apart.

Topics You May Be Interested In
Using And Converting Units Deriving Bernoullis Equation
Stress, Strain, And Elastic Moduli More On Gravitational Potential Energy
Elasticity And Plasticity The Motion Of Satellites
Pressure Gauges The Escape Speed From A Star
The Continuity Equation Summary

Topics You May Be Interested In
Center Of Gravity Gravitation And Spherically Symmetric Bodies
Finding And Using The Center Of Gravity Satellites: Circular Orbits
Pressure Gauges Kepler's Second Law
The Continuity Equation Black Holes, The Schwarzschild Radius, And The Event Horizon
Newton's Law Of Gravitation Amplitude, Period, Frequency, And Angular Frequency

Orbits: When a satellite moves in a circular orbit, the centripetal acceleration is provided by the gravitational attraction of the earth. Kepler’s three laws describe the more general case: an elliptical orbit of a planet around the sun or a satellite around a planet.

Topics You May Be Interested In
Uncertainty And Significant Figures Pressure Gauges
Center Of Gravity Solved Problems
Bulk Stress And Strain Why Gravitational Forces Are Important
Elasticity And Plasticity Periodic Motion
Fluid Mechanics Describing Oscillation

Topics You May Be Interested In
Center Of Gravity Gravitation
Tensile And Compressive Stress And Strain Kepler's Laws (firsts, Second, Third Laws) And The Motion Of Planets
Bulk Stress And Strain Black Holes
Elasticity And Plasticity Detecting Black Holes
Pressure In A Fluid Period And Amplitude In Shm

Black holes: If a nonrotating spherical mass distribution with total mass M has a radius less than its Schwarzschild radius RS, it is called a black hole. The gravitational interaction prevents anything, including light, from escaping from within a sphere with radius RS.

+
Ans: If light cannot escape from a black hole and if black holes are small . how can we know that such things exist? The answer is that any gas or dust near the black hole tends to be pulled into an accretion disk that swirls around and into the black hole, rather like a whirlpool view more..
+
Ans: At points far from a black hole, its gravitational effects are the same as those of any normal body with the same mass. If the sun collapsed to form a black hole, the orbits of the planets would be unaffected. But things get dramatically different close to the black hole. view more..
+
Ans: The first expression for escape speed in Eq. (13.29) suggests that a body of mass M will act as a black hole if its radius R is less than or equal to a certain critical radius. view more..
+
Ans: HERE ISA SUMMARY OF GRAVITATION , FOR QUICK REVISION view more..
+
Ans: Many kinds of motion repeat themselves over and over: the vibration of a quartz crystal in a watch, the swinging pendulum of a grandfather clock, the sound vibrations produced by a clarinet or an organ pipe, and the back-and-forth motion of the pistons in a car engine. This kind of motion, called periodic motion or oscillation view more..
+
Ans: n. A body with mass m rests on a frictionless horizontal guide system, such as a linear air track, so it can move along the x-axis only. The body is attached to a spring of negligible mass that can be either stretched or compressed. The left end of the spring is held fixed, and the right end is attached to the body. The spring force is the only horizontal force acting on the body; the vertical normal and gravitational forces always add to zero view more..
+
Ans: Here are some terms that we’ll use in discussing periodic motions of all kinds: view more..
+
Ans: The simplest kind of oscillation occurs when the restoring force Fx is directly proportional to the displacement from equilibrium x. This happens if the spring in Figs. 14.1 and 14.2 is an ideal one that obeys Hooke’s law view more..
+
Ans: To explore the properties of simple harmonic motion, we must express the displacement x of the oscillating body as a function of time, x1t2. view more..
+
Ans: the period and frequency of simple harmonic motion are completely determined by the mass m and the force constant k. In simple harmonic motion the period and frequency do not depend on the amplitude A. view more..
+
Ans: We still need to find the displacement x as a function of time for a harmonic oscillator. Equation (14.4) for a body in SHM along the x-axis is identical to Eq. (14.8) for the x-coordinate of the reference point in uniform circular motion with constant angular speed v = 2k/m view more..
+
Ans: We can learn even more about simple harmonic motion by using energy considerations. The only horizontal force on the body in SHM in Figs. 14.2 and 14.13 is the conservative force exerted by an ideal spring. The vertical forces do no work, so the total mechanical energy of the system is conserved. We also assume that the mass of the spring itself is negligible. view more..
+
Ans: the energy quantities E, K, and U at x = 0, x = ±A/2, and x = ±A. Figure 14.15 is a graphical display of Eq. (14.21); energy (kinetic, potential, and total) is plotted vertically and the coordinate x is plotted horizontally. The parabolic curve in Fig. 14.15a represents the potential energy U = 1/2 kx2 . The horizontal line represents the total mechanical energy E, which is constant and does not vary with x. view more..
+
Ans: PROBLEM SOLVING STRATEGY ON ENERGY MOMENTUM OF SHM view more..
+
Ans: So far, we’ve looked at a grand total of one situation in which simple harmonic motion (SHM) occurs: a body attached to an ideal horizontal spring. But SHM can occur in any system in which there is a restoring force that is directly proportional to the displacement from equilibrium, as given by Eq. (14.3), Fx = -kx view more..
+
Ans: A mechanical watch keeps time based on the oscillations of a balance wheel (Fig. 14.19). The wheel has a moment of inertia I about its axis. A coil spring exerts a restoring torque tz that is proportional to the angular displacement u from the equilibrium position. We write tz = -ku, where k (the Greek letter kappa) is a constant called the torsion constant. Using the rotational analog of Newton’s second law for a rigid body, gtz = Iaz = I d2 u>dt2 view more..
+
Ans: The following discussion of the vibrations of molecules uses the binomial theorem. If you aren’t familiar with this theorem, you should read about it in the appropriate section of a math textbook. view more..
+
Ans: A simple pendulum is an idealized model consisting of a point mass suspended by a massless, unstretchable string. When the point mass is pulled to one side of its straight-down equilibrium position and released, it oscillates about the equilibrium position. view more..

Rating - 4/5
467 views