Let t be the period of a planet about the sun; that is, t is the time required for it to travel once are 2a and 2b. (a) use part (d) of problem 1 to show that t-2tab/h (b) show that_-ed=-. 2. lliptical orbit. su h2 gm b2 cl 4t2 gm (c) use parts (a) and (b) to show that ta this proves kepler's third law. [notice that the proportionality constant 4? 9(gm) is inde- pendent of the planet.]

Suppose a force of 60 n is required to stretch and hold a spring 0.1 m from its equilibrium position. a. assuming the spring obeys hooke's law, find the spring constant k. b. how much work is required to compress the spring 0.5 m from its equilibrium position? c. how much work is required to stretch the spring 0.6 m from its equilibrium position? d. how much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium? a. kequals 600