# Every particle of matter in the universe attracts every other particle with a force that is directly

 Sana 11.10.2017 Hajmi 449 b. • ## A particle of mass m rotates with a uniform speed on the inside of a bowl’s parabolic frictionless surface in a horizontal circle of radius R = 0.4 meters as shown below. At the position of the particle the surface makes an angle θ = 17o with the vertical. What is the angular velocity of the particle? • ## To compare and understand the orbits of satellites and celestial objects • ## Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. • ## By contrast, capital G relates the gravitational force between any two bodies to their masses and the distance between them. Henry Cavendish measured the value of G in 1798. We call G a universal constant because it has the same value for any tow bodies, no matter where in space they are located.    • ## At the surface of the moon we consider a body’s weight to be the gravitational attraction of the moon, so on. • ## If we model the earth as a spherically symmetric body with radius RE and mass mE, the weight wof a small body of mass m at the earth’s surface is  • ## Suppose we drill a hole through the earth (radius RE, mass mE) along a diameter and drop a mail pouch (mass m) down the hole. Derive an expression for the gravitational force on the pouch as a function of its distance r from the center. Assume that the density of the earth is uniform. • ## Gravity (and hence, weight) decreases as altitude rises outside Earth and also decrease as approaching the center of Earth and becomes zero at the center of Earth. • ## We have used the fact that the earth is an approximately spherically symmetric distribution of mass. But this does not mean that the earth is uniform. In fact, the density of the earth decreases with increasing distance from its center. • ## Mass = 2 times the mass of the earth, radius = 4 times the radius of the earth. • ## Ball B (moment of inertial about its center ⅔ MR2), rolls down the distance x along the inclined plane without slipping. In terms of acceleration due to earth’s gravity g, what is the acceleration of ball B along the inclined plane? • ## MC packet: #21, 23, 24, 25, 32,36 • ## To determine the gravitational potential energy of an object at a height that is way above the earth’s surface, we need to calculate work done by the gravitational force on the object and use equation: • ## Note that U is relative. Only ∆U is significant.  • ## Extra credit on test – use the above equation to prove that near Earth’s surface the potential energy is            • ## 2nd Law: A line connecting the sun to a given planet sweeps out equal areas in equal times. • ## Eccentricity (e): a dimensionless number between 0 and 1. If e=0, ea=0, the ellipse is a circle.      • ## The orbit of Comet X has a semi-major axis that is four times larger than the semi-major axis of Comet Y . What is the ratio of the orbital period of X to the orbital period of Y? • ## 1/100 as great. • ## How far from a very small 150 kg ball would a particle have to be placed so that the ball pulled on the particle just as hard as the earth does? • ## What is the escape speed from an asteroid of diameter 255 km with a density of 2720 kg/m3 ? • ## Is it reasonable that you could actually set up this as an experiment? Why? • ## r2 – r1 = h (height above Earth’s surface) 