Problem 1 At some airshows a rocket engine is affixed to a portable toilet (port-a-potty) to propel it along the tarmac. In this problem, we consider such an unfortunate spectacle and ask ourselves the question - what if it tips over? R W/4 R,MA W/2 h 2 T,M Figure 1: Rocket Powered Outhouse As illustrated in Figure 1, a rocket motor is affixed to to the top left point (R) of the outhouse and applies force P = Pf2 at this point. The outhouse is supported on wheels located at S1 and S2, each of which apply a normal force to the system. These forces are and 2 respectively. We treat the entire system as having two point masses: one representing the heavy rocket with mass mR at R and another representing the mass my located at the vehicle CoM T. The outhouse has height h and width w and Figure 1 gives the relevant positional information. You may assume that the wheels are mass-less and have a r < (i) The sum of all external forces on the vehicle (represented in basis vectors of frame F). e.g. N1f3+ N1f3+ P2... (ii) Write all three equations we get from applying LMB to our system (one equation each for each of the three basis vectors of F.) (iii) What is 2 when we set N = 0? (b) We now want to find the maximum thrust magnitude P that will cause tipping. LMB does not give us enough information here so let us resort to AMB. (i) Pick a suitable point as the reference point for AMB. We will call this point Q henceforth. (ii) Find the moments of all external forces about Q. (iii) Compute the angular momentum of masses mr and mr about Q. (iv) If your point Q is moving with respect to frame F, find of mass of the full system. (Q) and (G) where G is the center (v) Write the AMB for this system and solve for P in terms of w, h, g, mr and mr. (c) If the 'vehicle' is accelerating at 10 m/s, mR = 8 kg, mR 15 kg, h g 9.8 m/s, will the 'vehicle' tip over? = 2 m, w 1 m and