(25 points)An automobile is trying to climb a hill covered with ice in winter. A thin film of water exists between the spinning tires and the ice. Assume that any

friction between the tires and ice is due to this water film and that no 'dry' frictional forces occur. The automobile's forward velocity up the hill is zero. It is a four-wheel drive vehicle and all four wheels are spinning. The angular rotation rate of the tires o necessary to keep the automobile stationary depends on the several parameters listed in the 1st column of the table. Fill in the table. Briefly explain your answers for the 4th column (Analysis Prediction) at the end of your solution for part b) below. You do not need to justify your answers for the rest of the table.a) b) Find an equation for the angular rotation rate a as a function of your listed parameters in part a). c) Find a numerical value for 0 if M = 1300 kg, 0 = 10 deg, R = 10 inches, H=0.5 mm, the contact area of each tire is 8 inches x 8 inches,, and the air (and water film) temperature is 1.0degrees Celsius. d) Based on the magnitude of your answer in part c), do you think the assumption of friction only due to the thin water film, e.g no 'dry' friction is a reasonable assumption? As the tires rotate they may increase the temperature of the water in the film. This, in turn, may affect other parameters in the problem? Do you think the required angular rotation rate o of the tire (to hold the automobile stationary) will; f) Why? e.g. clearly describe your physical reasoning for part e).