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

Answer 1

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.