Problem 1: Rotating Space Stations One problem for humans living in outer space is that they are apparently weightless. One way around this problem is to design a space station that spins about its center at a constant rate. This creates "artificial gravity" at the outside rim of the station. a) If the diameter of the space station is 800 m, how many revolutions per minute are needed for the "artificial gravity" acceleration to be 9.80 m/s-? b) If the space station is a waiting area for travelers going to Mars, it might be desirable to simulate the acceleration due to gravity on the Martian surface 3.70m/s'. How many revolutions per minute are needed in this case?Problem 2 A balky cow is leaving the barn as you try harder and harder to push her back in. In coordinates with the origin at the barn door, the cow walks from = = 0m to r = 6.9m as you apply a force with a-component Fi = (20.0N + (3.0N/m):x). How much work does the force you apply do on the cow during this displacement