In this paper it is shown that the change in the energy for a linearly viscoelastic body (with Kelvin-Voigt type viscosity) in frictionless contact with a rigid obstacle can be accounted for by viscous losses and the work done by external forces. Thus there is no change in the energy due to impacts, unlike the case of rigid-body dynamics. The result can be extended to a wide class of dynamic viscoelastic boundary thin obstacle problems of similar type.