1. The problem statement, all variables and given/known data You are building a remote control car. The car has 50 mm tire diameter, and you want the car to travel on level ground at a speed of 9 mph. You need to select a single motor and gear head for the project. Provide hand written calculations and answers to the following questions. Note: be sure to write out all units in your calculations, and perform any necessary unit conversations. a) To travel at the desired speed, what is the required angular velocity of the tires (in rpm and rad/s)? b) Assume an idealized system (no losses due to friction, no tire slippage, etc.), and that the car requires a constant force of 12 N to move across this particular ground condition. To achieve the desired speed what would be the minimum power (in watts) required for the car’s motor? c) Select a DC motor (from an online supplier, e.g., Maxon) that uses ≤24 V nominal voltage and has at least 10% more power output than what you calculated in part b. Provide the part number and also download and attach a copy of the motor’s specification sheet. d) Assume you wanted the motor to operate near peak efficiency (at about 25% of the stall torque), what gear reduction ratio would be needed to obtain the desired torque output at the tires (note: calculate the required torque first), again assuming an ideal lossless system? e) Find a gear head (gearbox) with appropriate reduction ratio (from an online supplier). Provide the part number and also download and attach a copy of the specification sheet. Try to find one which matches the motor shaft size. f) Check if the angular velocity output from the gear is still larger than the angular velocity required (which you calculated in part a). g) In this exercise we assumed an idealized system to select a motor and gear head. But in reality there are always some mechanical losses, and therefore power transmission will not be 100% efficient. Look on the data sheet for the gear head you selected and report the efficiency (often reported as maximum efficiency) of the gear head. 2. Relevant equations They are listed below. 3. The attempt at a solution a) v = rw, Solve for w. Is this right? b) P1 = Fv, Solve for P1. Is this right? c) P1=VI, Solve for I d) To=rF, Solve for To (torque output). What is stall torque? Is it the torque output? If not, how do I get it? G=win/wout How do I find win? e) f) g) Does the number of tires of the remote control car matter? Let's say there are 4 tires. How does it relate with the calculations?