Question

Use the principle of total energy to find the velocity which a body must be projected vertically, in the absence of air resistance, to rise to a height above the earth's surface that will equal the earth's radius we will call r. (you will leave everything in terms of the variables and you must tell me what each variable means - in this case that is why the answer given is just variables) b) explain what will happen to the velocity if the distance increases by 2. c) Explain what will happen to the velocity if the distance is decreased by 1/2. (v = Gm_e/r)

Answer 1

The gravitational potenti al energy of a object on the earths surface is GMm Here, G is universal gravitati onal constant,M is mass of earth and m is mass of object. R is radius of the earth The gravitational potential energy of a object at height (h) is equal to the radius of earth (R) measured from the earths surface is GMm 2R The expression for kinetic energy of the object is From energy conservati on principle кв-U2-U, GMm 2R 2R GM B)From the above equation v co decreases as If the di stance is doubled(2r).velocity becomes, which means orbital velocity distance from the planet (earth)increase V 2 (c)If the distance is halvedvelocity becomes