In order to properly control the physical interactive behavior of a flying vehicle, the information about the forces acting on the robot is very useful. Force/torque sensors can be exploited for measuring such information but their use increases the cost of the equipment, the weight to be carried by the robot and, consequently, it reduces the flying autonomy. Furthermore, a sensor can measure only the force/torque applied to the point it is mounted in. In order to overcome these limitations, in this paper we introduce a Lyapunov based nonlinear observer for estimating the external forces applied to a quadrotor. Furthermore, we show how to exploit the estimated force for shaping the interactive behavior of the quadrotor using Interconnection and Damping Assignment Passivity Based Controller (IDA-PBC). The results of the paper are validated by means of simulations.