A simple wheel and axle is used to lift the bucket of out of a well. The radii of the wheel and axle is 30 cm and 5 cm respectively. Determine the efficiency if the actual effort required is 20 N.
To determine the efficiency of the wheel and axle system, we need to first calculate the ideal mechanical advantage (IMA) and then use it to calculate the efficiency.
The IMA of a wheel and axle system is calculated using the ratio of the radii of the wheel to the axle. In this case, the radii of the wheel (R) and the axle (r) are 30 cm and 5 cm respectively:
IMA = R/r
IMA = 30 cm / 5 cm
IMA = 6
Next, we need to calculate the actual mechanical advantage (AMA) based on the actual effort required. Given that the actual effort is 20 N, we can calculate the AMA using the formula:
AMA = Actual Load / Actual Effort
AMA = load / effort
AMA = R/r = 30/5 = 6
Now we can calculate the efficiency of the wheel and axle system using the formula:
Efficiency = AMA / IMA * 100%
Efficiency = 6 / 6 * 100%
Efficiency = 100%
Therefore, the efficiency of the wheel and axle system is 100%. This means that the system is able to lift the load with the same amount of force as the effort applied.