The axle diameters of a differential wheel and axle lifting machine are 254mm and 129mm respectively. The load has a mass of 36kg and the effort required is 300N. If the efficiency is 45%, calculate the diameter of the wheel required
First, we need to calculate the mechanical advantage of the system using the formula:
Mechanical Advantage = Load / Effort
= 36kg / 300N
= 0.12
Next, we can calculate the ideal mechanical advantage of the system using the formula:
Ideal Mechanical Advantage = larger axle diameter / smaller axle diameter
= 254mm / 129mm
= 1.97
Now, we can use the efficiency formula to find the actual mechanical advantage of the system:
Efficiency = Mechanical Advantage / Ideal Mechanical Advantage * 100%
0.45 = Mechanical Advantage / 1.97 * 100%
Mechanical Advantage = 0.45 * 1.97
Mechanical Advantage = 0.885
Now, we can use the mechanical advantage formula to find the wheel diameter:
Mechanical Advantage = Wheel Diameter / larger axle diameter
0.885 = Wheel Diameter / 254mm
Wheel Diameter = 0.885 * 254mm
Wheel Diameter = 224.8mm
Therefore, the required diameter of the wheel is approximately 224.8mm.