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Answer :
The length required for the handle to lift the load with the given force is approximately 1683.18 inches.
Step-by-Step Explanation:
- First, calculate the circumference (C) of the screw using the formula C = π [tex]\cdot[/tex] diameter = 3.00 [tex]\cdot[/tex] π ≈ 9.42 inches.
- The pitch (P) is given as 0.125 inches. The mechanical advantage (MA) is therefore C / P = 9.42 / 0.125 = 75.36.
- Given that a person applies a force (F) of 80.4 pounds to the handle, the effort force (Fe) should balance the load force (Fl). Using the formula Fl = MA [tex]\cdot[/tex] Fe: Fl = 75.36 [tex]\cdot[/tex] 80.4 = 6058.82 pounds.
- Given the specified load of 135,428 pounds, the ratio of loads (Rl) is 135,428 / 6058.82 = 22.35.
- The lever arm should then multiply the effort by this ratio. So, we need to calculate the needed length (L) of the handle that applies the force appropriately: Fe [tex]\cdot[/tex] L = Fl. Using the force equilibrium L = 135,428 / 80.4 ≈ 1683.18 inches.
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