1. (5 points) A 3-kg plastic tank that has a volume of 0.2 m is filled with liquid water. Assuming the density of water is 1000 kg/m, determine the weight of the combined system. 2. (5 points) What is the difference between the analytical and empirical approach to engineering problems? Discuss the advantages and disadvantages of each approach. 3. (10 points) The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25C, the pressure gauge reads 210 kPa (Note that a pressure gauge provides the pressure relative to atmospheric pressure-so a gauge reading 1 atm of pressure at sea level has 2 atm of total or absolute pressure). If the volume of the tire is 0.025 m, determine the pressure rise in the tire when the air temperature in the tire rises to 50C. Also, determine the amount of air that must be bled off to restore pressure to its original value at this temperature. Assume the atmospheric pressure to be 100 kPa. 4. (10 points) Use Microsoft Excel or other appropriate software to create a scatter plot of the relationship between elevation and air density shown in the table below. Add a trend line fit of your choice to the plot and create an empirical model that predicts the density for a value of the elevation. Justify your choice of model fit to the data. The spreadsheet can be converted into a pdf by "printing to pdf," where it can be combined with the other problems. Elevation (km) Density (kg/m) 0 1 1.225 1.112 2 1.007 3 0.9093 4 0.8194 5 0.7364 6 0.6601 8 0.5258 10 0.4135 15 0.1948 20 0.08891 25 0.04008