Homework SourseIm having trouble solving this problem Help me please Perhap
I\'m having trouble solving this problem. Help me please.
Perhaps the most common automotive power gear-train arrangement is shown below. The engine produces a torque at an angular velocity (the \"tachometer\" engine speed) depending on how much gas is fed to the engine (which, in general, is not a simple linear relationship). The torque is transmitted to the rear wheels via the variable ratio transmission and then by the fixed-ratio differential (or \"rear end\") which also changes the of the power flow. Obviously we know that the engine must produce torque to accelerate the vehicle. However, even when the vehicle is operating at a constant speed, torque is required to overcome friction in the gear-train, wheel friction, wind resistance and to go up hills. Notice that, for a constant speed, the engine speed is constant and the engine is essentially in a state of equilibrium (that is, the resistance torque acting back on the engine must just equal the torque produced by the engine). I. If the tachometer is reading 2000 RPM and you are travelling 56 MPH in a vehicle with 0.8 m diameter tires, what is the overall gear-train ratio (ie combined transmission & differential ratios) from the engine to the drive wheels? II. If the engine is producing 600 Nm of torque, what torque is delivered to the drive wheels in the situation described in I above, Ignoring friction losses in the gear-train? III. If the vehicle weighed 13000 N and an estimated 2100 N are required to overcome tire friction, air resistance, etc at the speed it is traveling, how long would it take the vehicle to accelerate from 56 MPH to 60 MPH on a straight and level road?Solution
1) 56 Mph = 25.0342 m/s
Wtyre = 25.0342 / 0.4 = 62.5855 rad/s or 597.65 rpm
Gear ratio = 597.65 / 2000 = 0.298825
2) Tengine = 600 Nm
Tdrive = 600 / 0.298825 = 2007.86 Nm
3) Fdrive = Tdrive / r = 20007.86 / 0.4 = 5019.66 N
Net force = 5019.66 - 2100 = 2919.66 N
acceleration = 2919.66 / (13000/9.8) = 2.2 m/s^2
Vfinal = 60 mph or 26.8224 m/s
time = 26.8224 - 25.0342 / 2.2 = 0.81246 seconds
