A gymnast practices a handstand outside on two exercise platforms. A breeze is blowing in the positive x-direction and creates a distributed force Fbreeze along the length of her body. She abducts her left hip by 45 degrees while maintaining the handstand. In the model below, the total mass of torso and arms are treated as a point mass mtorso centered along the length of the torso, and the legs are treated as point masses mleg centered at the knees. The exercise platforms are assumed to be located directly below the shoulder joints, vertically aligned. Assume that the gymnast does not apply a moment on the platforms.
lknee = 0.40 m
Itorso = 0.60 m
larm = 0.60 m
Ihip = 0.15 m
Iclay = 0.15 m
lleg = 0.80 m
Mleg = 12.5 kg
mtorso = 35.0 kg
F breeze = 2.0 N/m
a) Given the anatomical dimensions and masses, determine forces FL and Fr at the gymnast's hands. Solve the problem symbolically first, then numerically, and show your work for each part.
b) The vertical supports for the exercise platforms are single 10.0 cm long hollow cylinders with outer diameters of 2.0 cm and inner diameters of 1.5 cm. If the support material has an elastic modulus of E = 100 GPa, how much will each of the exercise platforms move downward?
c) How strong would the breeze have to be to knock the gymnast of balance, causing her right hand to lift off the ground?