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Question

Using a wheel and axle machine, a force of 100 N applied to the rim of a wheel can lift a load of 80 kg .The diameters of the wheel and axle are 1 m and 80 cm respectively. Determine the actual mechanical advantage, and the efficiency of the machine.

Answer 1

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Answer 2

The ideal mechanical advantage is the ratio of the wheel diameter to the axle diameter which is  1/0.8 m = 1.25.

 

The actual mechanical advantage is the ratio of the delivered force to the applied force.  The applied force is 100 N, but the weight is 9.8 m/s * 80 kg =    784 N.   784/100 = 7.84.

 

Based on the numbers given, it appears that the problem is incorrectly formulated.   The actual mechanical advantage is greater than the ideal value using the numbers given.   Let's assume that the diameter of the wheel were instead 8 cm rather than 80cm.  In any event that seems a more reasonable axle size and gives a practical answer.   In that case the ideal mechanical advantage would be 12.5.   (1.0/0.08 = 12.5)

 

The efficiency of the machine would then by 7.84 / 12.5 or  59%.