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In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is _________.
- 40.00
- 46.02
- 60.01
- 92.02
Correct answer: 46.02
Solution
The relationship between load and cycles to failure is exponential, meaning that as the load decreases, the number of cycles until failure increases significantly. Given the data points, we can derive the load corresponding to 5000 cycles by interpolating between the known values of 100 cycles at 80 units and 10000 cycles at 40 units, leading to the conclusion that the load for 5000 cycles is approximately 46.02 units.
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