There is a big rug MR = 20.0 kg sitting on a slope # = 26.0" here on earth. A novel Pokemon goat Me = 40.0 keg decides to slide on the rug. The goat is sliding uphill on top of the rug, and the rug is not sliding on the sloped tile floor. The goat and the rug have coefficient of kinetic friction / = 0.300 The rug and the tile floor have coefficient of static friction , = 0.700 3. (10 points) Draw a free-body diagram for each of the following: a. The goat b. The rug* (Did you include your coordinate system and net force vectors?) (5 points) Referring to your FBDs, write the equations you get from Newton's second law in your two coordinate directions for each of the following. You will have four equations in total. a. The goat b. The rug 5. (10 points) While the goat is sliding uphill: a. Calculate the magnitude of the acceleration of the goat. What direction is the acceleration of the goat? b. Calculate the magnitude of the static frictional force f between the rug and the tile floor. Does f point uphill or downhill? 6. (5 points bonus and a sticker on your exam) a. If you could change # while keeping all other quantities the same, what angle would result in the maximum acceleration of the goat? * You do not know whether f points uphill or downhill until completing question 5. For f in questions 3 & 4, either direction is ok as long as your signs are consistent