College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Chapter 5, Problem 29PE
During a circus act, one performer swings upside down hanging from a trapeze holding another, also upside-down, performer by the legs. If the upward force on the lower performer is three times her weight, how much do the bones (the femurs) in her upper legs stretch? You may assume each is equivalent to a uniform rod 35.0 cm long and 1.80 cm in radius. Her mass is 60.0 kg.
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During a circus act, one performer swings upside down hanging from a trapeze holding another, also upside-down, performer by the legs. If the upward force on the lower performer is three times her weight, how much do the bones (the femurs) in her upper legs stretch? You may assume each is equivalent to a uniform rod 35.0 cm long and 1.80 cm in radius. Her mass is 60.0 kg.
When a gymnast weighing 740 N executes the iron cross as in figure (a), the primary muscles involved in supporting this position are the latissimus dorsi ("lats") and the pectoralis major ("pecs"). The rings exert an upward force on the arms and support the weight of the gymnast. The force exerted by the shoulder joint on the arm is labeled
Fs
while the two muscles exert a total force
Fm
on the arm. Determine the magnitude of the force
Fm.
Note that one ring supports half the weight of the gymnast, which is w = 370 N as indicated in figure (b). Assume that the force
Fm
acts at an angle of 45° below the horizontal at a distance of 4.0 cm from the shoulder joint. In your estimate, take the distance from the shoulder joint to the hand to be L = 71 cm and ignore the weight of the arm.
1. During a circus act, one performer swings upside down hanging from a trapeze holding another, also
upside-down, performer by the legs. If the upward force on the lower performer is three times
their weight, how much do the bones (the femurs) in their upper legs stretch? You may assume each
is equivalent to a uniform rod 35.0 cm long and 1.80 cm in radius. Her mass is 65.0 kg. The Young's
modulus for bones is 1.6 x 1010 N/m².
Think & Prepare
1. For this problem, assume that the leg bones are uniform rods.
2. What kind of stress does the legs of the trapeze artist experience? Tensile, compressive or shear
stress? How will you fund the cross-sectional area of the bone?
3. What type of elastic modulus is appropriate for this problem?
4. If the total upward force on the artist is given, what is the force on each leg?
Enter to 3 significant figures
Amount by which the femurs stretch
=
cm
Reflect: Is this stretch large or small? Compare it to the length of the leg.
Chapter 5 Solutions
College Physics
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