A. IMA: 4
The Ideal Mechanical Advantage (IMA) is given by:
[tex]IMA = \frac{d_i}{d_o}[/tex]
where
[tex]d_i[/tex] is the input distance
[tex]d_o[/tex] is the output distance
For the pulley system in this problem, [tex]d_i = 3.90 m[/tex] and [tex]d_o = 0.975 m[/tex], so the IMA is
[tex]IMA=\frac{3.90 m}{0.975 m}=4[/tex]
B. MA: 3.59
The actual mechanical advantage (AMA), or simply the Mechanical Advantage (MA), is given by
[tex]MA=\frac{F_o}{F_i}[/tex]
where [tex]F_o[/tex] is the output force and [tex]F_i[/tex] is the input force. For the pulley system in this problem, [tex]F_i = 375 N[/tex] and [tex]F_o = 1345 N[/tex], so the MA is
[tex]MA=\frac{1345 N}{375 N}=3.59[/tex]
C. Efficiency: 89.8 %
The efficiency of a machine is equal to the ratio between the MA and the AMA:
[tex]\eta = \frac{MA}{AMA} \cdot 100[/tex]
Therefore, in this case,
[tex]\eta=\frac{3.59}{4}\cdot 100=0.898=89.8 \%[/tex]
