In the arabesque position an initially upright gymnast kicks one leg backward and upward while keeping it straight (mass m_leg), pushes her torso and head forward (mass m_torso+head), and propels her arms backward and upward while keeping them straight (each m_arm). They, respectively, make acute angles θ_leg, θ_torso+head, and θ_arms, to the horizontal. The centers of mass of the extended leg and vertical balancing leg are x_extended-leg and x_balancing-leg behind the vertical from the center of mass (in the midsagittal plane), and that of her upper body (torso/head/arms combination) is x_upper-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 ybeforeto 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 (4ft 11in) tall and has a mass of 38kg (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.)
(d) Redo Problem if the free leg of the gymnast is horizontal and her arms are vertical. (This is the cheerleading position.)
