1. I need some help with my riding lawn mower. In the table that I have above yo

Question

1. I need some help with my riding lawn mower. In the table that I have above you should be able to calculate the following problem. Can you determine the power that is required, in watts, for the drive motor to overcome friction and operate at this speed. Recall that work is the force delivered over the distance and that power is energy in a specific amount of time. You can assume the frictional coefficient includes rolling resistance, cutter resistance, drag etc.

Ariens 42 in 17hp riding mower spec value Mass with rider 260kg Rear wheel radius 20cm Gas engine power 17hp Gas engine max temp 877k Ambient temp 293k Gas engine efficiency 0.5 of carnot Gas engine RPM 1500RPM Two cutting DC motor, power, each 500W Cutter blade RPM 1000RPM Cutter blade radius 20cm Runtime requirement, hours 2.8 hours 1.440 kWh batter mass 27kg Max speed required 3m/s Estimated coefficient of friction while mowing 0.1

Explanation / Answer

Friction force = mu* m * g   = 0.1 * (27 + 260) * 9.8 = 281.26 N

Friction Power   = Friction Force * Cutting Speed

                        = 281.26 * (pi * 1000 / 30 ) * 0.2    =   5.89 KW

Power required to drive mower (operate at this speed) = Friction force * Velocity

                                              = 281.26 *3 = 0.844 kW

Total power required for cutting and operation = 0.844 + 5.89   = 6.734 kW

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