Final answer:
To calculate the overall AMA of a system of two levers, multiply the individual AMAs and then apply the overall efficiency. However, the calculated AMA does not match any of the given options, indicating a possible error in the question or choices.
Step-by-step explanation:
The question asks to determine the overall Actual Mechanical Advantage (AMA) of a system consisting of two levers with different efficiencies and AMAs. To find the overall AMA, you would typically multiply the AMAs of the individual levers. However, since each lever has an efficiency less than 100%, you need to account for the loss in efficiency in the calculation.
The AMA of the first lever is 5.20 and has an efficiency of 85%, while the second lever has an AMA of 7.40 with an efficiency of 80%. Multiplying the AMAs together gives you the combined AMA without considering efficiency. To include efficiency, you multiply each lever's AMA by its efficiency (as a decimal) before combining them:
First Lever Effective AMA = 5.20 × 0.85 = 4.42
Second Lever Effective AMA = 7.40 × 0.80 = 5.92
To find the overall AMA of the system, you would then multiply the Effective AMAs of both levers:
Overall AMA = 4.42 × 5.92 = 26.1664
However, since none of the given choices match the result, this indicates a misstep in the method. The correct procedure would be to multiply the AMAs together and then apply the combined efficiency of both levers:
Overall Efficiency = 0.85 × 0.80 = 0.68
Combined AMA = 5.20 × 7.40 = 38.48
Applying overall efficiency to the combined AMA:
Overall AMA of the system = 38.48 × 0.68 = 26.1664
In conclusion, the overall AMA cannot be directly determined from the provided options A, B, C, and D since the calculated overall AMA does not match any of them. A re-evaluation of the problem or its given choices may be required.