CATAGORY: Mechanics QUESTION: A 50kg high wire artist carries a weighted pole as illustrated. Her center of gravity is 80cm above the high wire and the two 23kg masses are located 120cm vertically below the wire. Find the vertical location of the center of gravity of the walker and the weighted pole relative to the high wire. Is this case of stable or unstable equilibrium.

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The y component of the center of mass Y is calculated by approximating
the system as being made of three components.  The first the 50kg
wire walker whose center of mass is 80cm ABOVE the wire and two 23kg
masses 120cm BELOW the wire.  The y center of mass formula for a
three component system is

_    m(1) Y(1) + m(2) Y(2) + m(3) Y(3)
(1)  Y  = ----------------------------------
m(1) + m(2) + m(3)

Where m(1), m(2) and m(3) are the masses of the parts and Y(1), Y(2)
and Y(3) are the positions of the centers of mass of each of the
constitutient parts.   Now consider the figure below.

\||/
{..}
50kg  \/
/##\  ---- 80cm
| ## |
+    +O++++O+   +
+                  ||                   +
+                       \/                         +
________________________________________ 0cm__________________________
+                                                          +

+                                                             +

[ ] 23kg                            ---- -120cm           23kg  [ ]

Let Y(1) =   80cm , m(1) = 50kg
Y(2) = -120cm , m(2) = 23kg
Y(3) = -120cm , m(3) = 23kg

Note the minus sign on the positions of the 23kg masses.
They are negative because they are below the wire.

Then

_    50kg 80cm + 23kg(-120cm) + 23kg(-120cm)      1520 kg cm
(2)  Y  = ---------------------------------------  = - -----------
50kg + 23kg + 23kg                         96 kg

= -15.8cm

*******************
*   _             *
*   Y = -15.8cm   *
*                 *
*******************

The system is stable because the center of gravity is below the wire.

CATAGORY: Mechanics QUESTION: A patient is in neck traction with skull calipers, as illustrated. Finf the maximum value of the suspended mass that will cause no tension or other force in the neck given that the mass of the head is 4.2 kg and the coefficient of friction between the head and the bed is o.20. (The angle between the horizontal and the force is 15 degrees.)