An architecture student working at a drafting table requires some muscle action

Question

An architecture student working at a drafting table requires some muscle action in order to support her head. As shown in the figure, three forces act on her head. If the force provided by muscles is

FM = 75 N

and the weight of her head is

W = 40 N,

determine the magnitude and direction of the force provided by the upper vertebrae

to hold her head stationary. Assume that this force acts along a line through the center of mass of her head as do the weight and muscle force. (Assume the +x-axis to be to the right.)

Explanation / Answer

here

Fm = 75 N

W = 40 N

from the mathematical property Q = 50

so the resultant force Fv may calculated by vecotor's rectanguler rule

Fv = sqrt(F2m + W2+2 x Fm x W x cosQ)

=sqrt(752 + 402 + 2*75*40*cos(50) )

= 114.082 N Ans

here the direction is given by

aelpha = tan-1( W x sinQ / Fm + W x cosQ)

= tan-1( 40 x sin50 / 75 + 40 xcos50 )

= tan-1 (-0.09238)

= -0.092118o from force Fm   Ans

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