This paper proposes a global sliding mode observer for a class of nonlinear mechanical systems with two degrees of freedom. For the observer design, besides the usual Coriolis and centrifugal forces, we consider (discontinuous) dry and viscous friction and non vanishing uncertainties/perturbations. Moreover, the system is not required to be bounded-input-bounded-state, rendering the observer design problem challenging. For this class of systems, a dissipativity-based sliding-mode observer, with theoretically exact global finite-time convergence to the actual velocities, is proposed. To illustrate the effectiveness of the proposed observer, experimental results on a cart-pendulum system are presented.