1. A simplified model of a rear wheel drive vehicle accelerating from rest is shown in Figure 1. G Gearbox W Motor 57 Tmotor F P Twheel r We consider that the vehicle is powered by a PMG 132 drive motor that has a stall torque of t = 2406 lbf - in with a no-load speed of wn = 3590 RPM. 3000 T 2500 S (1) ant 2000 1500 1000 500 0 0 500 1000 1500 PMG 132 2000 Motor Speed (rpm) -Torque-Power 2500 3000 Gear 3 3500 Wn Gear 2 40 35 30 Gear 1 25 20 15 10 5 0 4000 The torque-speed curve of the electric motor is shown in Figure 2. The angular velocity of the motor is wmotor. The power from the motor is transmitted to the wheels by a DANA H12 FNR gearbox. The gear box consists of a following gear train shown in Figure 3. Gear 4 Input Power (hp) Output Gear 1 has 24 teeth. Gear 2 has 72 teeth. Gear 3 has 24 teeth. Gear 4 has 106 teeth. The mass moment of inertia for each wheel is I = 1367 lbm - in.The radius of the drive wheel is r = 11 in. The angular velocity of the wheels is @wheel- The vehicle weighs W = 400 lbf. The acceleration of gravity is g = 386.2 in/s. (a) Derive the relationship between the torque on the rear wheel to its angular acceleration using the torque-speed curve of the motor, and Newton's laws applied to the vehicle. The equation should take the form @=-w+k Where, and k are constants obtained from the properties of the motor, the weight of the vehicle, the moment of inertia of the wheels, and the transmission design. (b) The solution to the equation above is w (t) = A e-t + k Where the value of A is obtained by using the initial conditions Wwheel 0 at time t = 0. Use this formula to compute the angular velocity of the drive wheels w wheel as a function of time. (c) The coefficient of friction is = 0.8. The lengths p and q are p = 19 in and q = 35 in. Will the wheels slip at w = 0 RPM?