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Balancing Moments
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Moment of Force
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Basic Machines - Intro to machines and motion theories
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Figure 3-5.-A practical application.

Figure 3-4.-Using the capstan. of the axle is L1. Then, EI x LI is the moment of force. You’ll notice that this term includes both the amount of the  effort  and  the  distance  from  the  point  of  application of  effort  to  the  center  of  the  axle.  Ordinarily,  you measure the distance in feet and the applied force in pounds. Therefore, you measure moments of force in foot- pounds (ft-lb). A moment of force is frequently called a moment. By using a longer capstan bar, the sailor in figure 3-4  can  increase  the  effectiveness  of  his  push  without making a bigger effort. If he applied his effort closer to the head of the capstan and used the same force, the moment  of  force  would  be  less. BALANCING MOMENTS You know that the sailor in figure 3-4 would land flat on his face if the anchor hawser snapped. As long as nothing breaks, he must continue to push on the capstan bar. He is working against a clockwise moment of force that is equal in magnitude, but opposite in direction, to his counterclockwise moment of force. The resisting moment, like the effort moment, depends on two factors. In  the  case  of  resisting  moment,  these  factors  are  the force (Rz) with which the anchor pulls on the hawser and the distance (L-J from the center of the capstan to its rim. The existence of this resisting force would be clear if the sailor let go of the capstan bar. The weight of the anchor pulling on the capstan would cause the whole works to spin rapidly in a clockwise direction—and good-bye anchor!  The  principle  involved  here  is  that  whenever the counterclockwise and the clockwise moments of force are in balance, the machine either moves at a steady speed or remains at rest. This idea of the balance of moments of force can be summed up by the expression CLOCKWISE COUNTERCLOCKWISE MOMENTS MOMENTS Since  a  moment  of  force  is  the  product  of  the amount of the force times the distance the force acts from the center of rotation, this expression of equality may be written El  x   ~]   =Ezx   L2, in that EI   = force of effort, L1    = distance from fulcrum or axle to point where  you  apply  force, Ez   = force of resistance, and h= distance from fulcrum or center axle to the  point  where  you  apply  resistance. EXAMPLE 1 Put this formula to work on a capstan problem. You grip a single capstan bar 5 feet from the center of a capstan head with a radius of 1 foot. You have to lift a 1/2-ton anchor. How big of a push does the sailor have to exert? First, write down the formula Here LI=5 Ep   = 1,000  pounds,  and L2=l. Substitute  these  values  in  the  formula,  and  it becomes: E1   X5= 1,000  x  1 and = 200 pounds 3-3

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