notes001 (21)

notes001 (21) - Joules, we must have j F j = 100 : 2 p 2...

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September 2, 2009 NAME____________________________________________ A wrench that is 0 : 4 meters long lies along the positive x axis and grips a bolt at the origin. A force is applied in the direction of the vector 1 ; 1 i . Find the magnitude of the force needed to supply 100 Joules of torque to the bolt. Solution 1 (the hard way): Recall that the torque is = r ± F where r F is the force vector. In this problem, the wrench vector is r = 0 : 4 i and the force vector is F = j F j cos (225 ) i + j F j sin (225 ) j = p 2 2 j F j ( i + j ) . We now see that = r ± F = (0 : 4 i ) ± p 2 2 j F j ! ( i + j ) ! = (0 : 4) p 2 2 j F j ! ( i ± ( i + j )) = & 0 : 2 p 2 j F j ( i ± i + i ± j ) = & 0 : 2 p 2 j F j ( 0 + k ) = & 0 : 2 p 2 j F j k . Hence j j = j r ± F j = & 0 : 2 p 2 j F j k = 0 : 2 p 2 j F j . In order to have j j = 100
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Unformatted text preview: Joules, we must have j F j = 100 : 2 p 2 353 : 55 Newtons. 1 Solution 2 (the easy way): Recall that the magnitude of the torque is j & j = j r jj F j sin ( ) where r is the &wrenchvector, F is the force vector, and is the angle between r and F . In this problem, the wrench vector is r = 0 : 4 i and hence j r j = 0 : 4 . Also = 135 & . Therefore j & j = 0 : 4 j F j sin (135 & ) or j & j = 0 : 2 p 2 j F j . In order to have j & j = 100 Joules, we must have j F j = 100 : 2 p 2 & 353 : 55 Newtons. 2...
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notes001 (21) - Joules, we must have j F j = 100 : 2 p 2...

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