Considering first that the machine is an ideal one with no friction: Note that s

Question

Considering first that the machine is an ideal one with no friction: Note that since three cords support the weight, when F moves down 3 m, the weight will move up only 1 m. a. What is the ideal mechanical advantage of this system? b. If the weight is raised 7.5 m, through what distance must F move? m c. If the weight is 54 N, what F would be required if there were no friction acting in the system? N d. With no friction, for 8 J of work input into the machine, how much work is output? J Now, considering that the machine is real, with some friction: e. If a 23.48 N force were required to move the weight, what would be the actual mechanical advantage? f. What is the efficiency of the machine under the condition in e? (Express this efficiency as a decimal.) g. If the efficiency of the system were 80%, what force now will be required to move the weight? N h. For the actual machine at 80% efficiency, if 8 of work is input into the machine, how much work is output? J

Explanation / Answer

a. 3 b. Mechanical advantage = Force distance / Object distance Force distace = 3*7.5 = 22.5m c. Mechanical advantage = Weight lifted/ Force used Force used = 54/3 = 18N d. Mechanical advantage = Output work/ Input work Output work = 8*3 =24J e. Actual mechanical advantage = 54/23.48 = 2.3 f. Efficiency = actual MA/ ideal MA = 2.3/3 = 77% g. Actual MA = Eff*ideal MA = 3*0.8 = 2.4 Force used = 54/2.4 = 22.5 N h. work output = 8*2.4= 19.2J

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