Jumping hoops

We investigate the dynamics of an elastic hoop as a model of the jumps of small insects. During a jump the initial elastic strain energy is converted to translational, gravitational, and vibrational energy, and is dissipated by interaction with the floor and the ambient air. We show that the strain energy is initially divided into translational, vibrational, and dissipation energies with a ratio that is constant regardless of the dimension, initial deflection, and the properties of a hoop. This novel result enables us to accurately predict the maximum jump height of a hoop with known initial conditions and drag coefficient without resorting to a numerical computation. Our model reduces the optimization of the hoop geometry for maximizing the jump height to a simple algebraic problem. (C) 2012 American Association of Physics Teachers. [DOI: 10.1119/1.3633700]