Question

A man holds a 194-N ball in his hand, with the forearm horizontal (see the figure). He can support the ball in this position because of the flexor muscle force M, which is applied perpendicular to the forearm. The forearm weighs 18.5 N and has a center of gravity as indicated. Find (a) the magnitude of M and the (b) magnitude and (c) direction (as a positive angle counterclockwise from horizontal) of the force applied by the upper arm bone to the forearm at the elbow joint. Upper arm bone Flexor muscle Elbow joint 0.0510 m-į"T-0.0890 m į 0.330 m

Answer 1

Let Fu be the force applied by upper arm bone

First find $\vec{M}$

Take moment about elbow joint

$\sum E=0$

$\vec{M}$ *0.051 -18.5*(0.051+0.089) - 194*0.33 =0

$\vec{M}$ *0.051 -2.59 - 64.02 =0

$\vec{M}$ = 66.61/0.051

$\vec{M}$ = 1306.08N

a) ANSWER: $\vec{M}$ = 1306.08N

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Consider all forces in vertical direction

$\sum Fy=0$

$\vec{M}$ -194-18.5 -Fu =0

Fu = $\vec{M}$ -194-18.5

Fu = 1306.08  -194-18.5

Fu = 1093.58 N

b)ANSWER: Fu = 1093.58 N

c)90 deg (vertically downwards)