BIO When a gymnast performing on the rings executes the iron cross, he maintains the position at rest shown in Figure P10.85a. In this maneuver, the gymnast’s feet (not shown) are off the floor. The primary muscles involved in supporting this position are the latissimus dorsi (“lats”) and the pectoralis major (“pecs”). One of the rings exerts an upward fore F → h on a hand as shown in Figure P10.85b. The force F → s is exerted by the shoulder joint on the arm. The latissimus dorsi and pectoralis major muscles exert a total force F → m on the arm. (a) Using the information in the figure, find the magnitude of the force F → m . (b) Suppose an athlete in training cannot perform the iron cross but can hold a position similar to the figure in which the arms make a 45° angle with the horizontal rather than being horizontal. Why is this position easier for the athlete? Figure P10.85
BIO When a gymnast performing on the rings executes the iron cross, he maintains the position at rest shown in Figure P10.85a. In this maneuver, the gymnast’s feet (not shown) are off the floor. The primary muscles involved in supporting this position are the latissimus dorsi (“lats”) and the pectoralis major (“pecs”). One of the rings exerts an upward fore F → h on a hand as shown in Figure P10.85b. The force F → s is exerted by the shoulder joint on the arm. The latissimus dorsi and pectoralis major muscles exert a total force F → m on the arm. (a) Using the information in the figure, find the magnitude of the force F → m . (b) Suppose an athlete in training cannot perform the iron cross but can hold a position similar to the figure in which the arms make a 45° angle with the horizontal rather than being horizontal. Why is this position easier for the athlete? Figure P10.85
BIO When a gymnast performing on the rings executes the iron cross, he maintains the position at rest shown in Figure P10.85a. In this maneuver, the gymnast’s feet (not shown) are off the floor. The primary muscles involved in supporting this position are the latissimus dorsi (“lats”) and the pectoralis major (“pecs”). One of the rings exerts an upward fore
F
→
h
on a hand as shown in Figure P10.85b. The force
F
→
s
is exerted by the shoulder joint on the arm. The latissimus dorsi and pectoralis major muscles exert a total force
F
→
m
on the arm. (a) Using the information in the figure, find the magnitude of the force
F
→
m
. (b) Suppose an athlete in training cannot perform the iron cross but can hold a position similar to the figure in which the arms make a 45° angle with the horizontal rather than being horizontal. Why is this position easier for the athlete?
In general it is best to conceptualize vectors as arrows in
space, and then to make calculations with them using
their components. (You must first specify a coordinate
system in order to find the components of each arrow.)
This problem gives you some practice with the
components.
Let vectors A = (1,0, -3), B = (-2, 5, 1), and
C = (3,1,1). Calculate the following, and express your
answers as ordered triplets of values separated by
commas.
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