  We extend the Jacobi structure from $TQ\times \mathbb{R}$ and $T^{*}Q \times
\mathbb{R}$ to $A\times \mathbb{R}$ and $A^{*}\times \mathbb{R}$, respectively,
where $A$ is a Lie algebroid and $A^{*}$ carries the associated Poisson
structure. We see that $A^*\times \mathbb{R}$ possesses a natural Jacobi
structure from where we are able to model dissipative mechanical systems,
generalizing previous models on $TQ\times \mathbb{R}$ and $\mathfrak{g}\times
\mathbb{R}$.
