Physics 315: Medical Physics -
Homework #1: Fun with statics
Due Tuesday, February 13th at 11:00 AM on paper
(1) In the arabesque position on the right an initially upright
ballerina kicks one leg backward and upward while keeping it
straight (mass mleg), pushes her torso and head forward (mass
mtorso+head), and propels her arms backward and forward while
keeping them straight (each marm). They, respectively, make
acute angles θleg, θtorso+head, and ±θarms, to the horizontal. The
centers of mass of the extended leg and vertical balancing leg
are xextended-leg and xbalancing-leg behind the vertical from the center
of mass (in the midsagittal plane), and that of her upper body
(torso/head/arms combination) is xupper-body in front of this
vertical (so all of these distances are defined as positive). In
achieving this arabesque position her center of mass drops
vertically from height ybefore to yafter.
(a) Draw a diagram showing the gymnast before and during this maneuver.
(b) Find the equilibrium condition in terms of these masses and distances. (Hint: Analyze
the torques about her center of mass in the arabesque position.You can ignore the
contribution from her arms. Why? You may not need all of the information that is
presented.)
(c) Assume the gymnast is 1.49m (4 ft 11 in) tall and has a mass of 38 kg (weight 84 lb)
and her free leg and arms make a 30◦ angle with the horizontal. What angle does her upper
body make with the horizontal? (Assume the anthropometric relations for a standard
human.)
(2) The distance from your instructor’s elbow to the middle of his hand is 34cm. He has a 25 kg
weight in his hand, and his arm and hand together weigh 1.5 kg. His bicep muscle attaches 4cm
from his elbow.
(a) What minimum force does his bicep muscle have to exert to lift this weight? Be sure
to draw a force diagram.
(b) Assuming that the bicep muscle does not exert a different force at different lengths,
does the angle that the elbow takes affect the minimum force required to lift the weight.
Demonstrate your answer.
(c) 7 foot 6 inch basketball player Yao Ming’s forearm + half-hand distance is 76 cm. His
arm and hand together weigh 2.1 kg. Assuming that his bicep attachment point is still 4cm
from the elbow, what force does his muscle have to exert to lift the same weight? How
much does this change if his attachment point is 6 cm from his elbow?
