Dancing around. Imagine a couple dancing in a circle. The couple hold hands and have their feet together on the floor, and we imagine their mass completely at their shoulders, as shown in drawing, and the normal force on the legs is parallel to the legs.
a.) Estimate the height of the shoulders above the ground and the radius of their arm reach. Draw a free body diagram of the forces acting on the dancer on the right, using T for tension and N for the normal force.
b.) Assuming they are standing still, write symbolic x and y equations of force.
c.) Estimate the tension, in newtons, in the dancer's arm when they are standing still. .
d.) Now suppose the dancers are circling with their feet at a fixed position on the floor while maintaining the geometry of the figure. Write the symbolic y-equation for the tension in the rightmost dancer's arm. Get all the signs right by asking yourself if the tension is increased when circling compared to standing still.
e.) If the dancers want to circle at one cycle per second, what tension, in newtons, is required in the arms?
f.) If the dancers are to go from rest to circling one cycle per second in an elapsed time of 2 seconds, what is the required tangential acceleration?
g.) Why could, or could not, the dancers circle at one cycle per second?