Apoint mass- half the mass of the earth is initially located at an altitude - the radius of the earth. the gravitational interaction between the point mass and the earth pulls them toward each other. let the initial velocities of both bodies were zero given mass of earth-6 x1024kg, radius of the earth-6.4x106m, the universal gravitation constant g-6.67x10-11n-m/kg2. (a) locate the center of mass (cm) of this system, initially how far is the cm from the center of the earth? (b) what is the speed of each body immediately before impact? (c) how far did the point mass move and how far did the earth move from initial time to impact? (d) set up the newton's second law equation for the point mass and that for the earth using the cm as the origin of your coordinate system (e) the differential equation in (d) is not easy to solve analytically, but you can solve them numerically with a computer. method: you know initial position of both bodies => you can find force acting on the bodies=> you can find the initial accelerations of each body -> to find the position and velocity of each body at small increment of time later, you assume the acceleration is constant during that small time interval=> once you have the new positions, you can find the new values for the forces and accelerations and keep propagating the process. (i will show you the procedure for a similar problem in class) solve the equations numerically and find the time of impact. (you can check how accurate your computer code is by comparing the distance travel by the two bodies from this method with the exact result of part c.

relativism, roughly put, is the view that truth and falsity, right and wrong, standards of reasoning, and procedures of justification are products of differing conventions and frameworks of assessment and that their authority is confined to the context giving rise to them. more precisely, “relativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have (e.g., beautiful, morally good, epistemically justified) not simpliciter, but only relative to a given framework of assessment (e.g., local cultural norms, individual standards), and correspondingly, that the truth of claims attributing these properties holds only once the relevant framework of assessment is specified or supplied. relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.

relativism has been, in its various guises, both one of the most popular and most reviled philosophical doctrines of our time. defenders see it as a harbinger of tolerance and the only ethical and epistemic stance worthy of the open-minded and tolerant. detractors dismiss it for its alleged incoherence and uncritical intellectual permissiveness. debates about relativism permeate the whole spectrum of philosophical sub-disciplines. from ethics to epistemology, science to religion, political theory to ontology, theories of meaning and even logic, philosophy has felt the need to respond to this heady and seemingly subversive idea. discussions of relativism often also invoke considerations relevant to the very nature and methodology of philosophy and to the division between the so-called “analytic and continental” camps in philosophy. and yet, despite a long history of debate going back to plato and an increasingly large body of writing, it is still difficult to come to an agreed definition of what, at its core, relativism is, and what philosophical import it has. this entry attempts to provide a broad account of the many ways in which “relativism” has been defined, explained, defended and criticized.

explanation:

molecules are free to separate from each other and will take on the shape of the container. molecules move completely at random and high speeds. they vibrate in a fixed position and do not move around much. molecules expand to the edge of their container.

80cm/s.

24cm/s.

53.3cm/s.