Apulley system lifts a 1345 n weight a distance of 0.975m. paul pulls the rope a distance of 3.90m, exerting a force of 375n. a. what is the ideal machine advantage of the system? b. what is the mechanical advantage? c. how efficient is the system?

A. IMA: 4

The Ideal Mechanical Advantage (IMA) is given by:

where

is the input distance

is the output distance

For the pulley system in this problem, and , so the IMA is

B. MA: 3.59

The actual mechanical advantage (AMA), or simply the Mechanical Advantage (MA), is given by

where is the output force and is the input force. For the pulley system in this problem, and , so the MA is

C. Efficiency: 89.8 %

The efficiency of a machine is equal to the ratio between the MA and the AMA:

Therefore, in this case,

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s