The positions of two masses, ma and mb, are described by the equations: a(t) = 3A sin (4wt) and x(t) = 2A sin (3wt). (a) Not including t = 0, what are the first three times that the masses will pass through their respective equilibrium positions simultaneously? (b) Find the two expressions that would describe each mass' velocity. What were the velocities at the times you found in part a?
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- One type of engine used in space travel is an ion thruster. These engines produce a low force that results in small acceleration changes. If an ion-thrust engine is used to apply 87 millinewtons [mN] of force on a satellite with a mass of 1.7 megagrams [Mg], what is the acceleration produced in units of meters per second squared [m/s2]?This time the quantities will be different, again randomly chosen by the computer. The mass will be much smaller for a different reason. The shell is thin, but has a definite thickness. Calculate the (volume) density of the shell, in g/cm3. Here are the numbers: R = 27 cm M = 800 grams thickness = 0.4 mmNewton's universal law of gravitation can be stated as the force F of gravitation between two objects varies jointly as the masses m, and m, of the objects, and Gm,m2 inversely as the square of the distance r between their centers, where G is the constant of proportionality. In other words, F = The weight of an object is the force F on the object due to gravity, where F = mg. State how g (the acceleration due to gravity) varies with respect to the mass m, of the spherical body on which the object lies, and the radius of that body (assume all of the mass is at its center.). The acceleration due to gravity, g, varies as the spherical body's mass, and as
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