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A module that is projective and torsion-free but not faithfully flat?

Let $R$ be a (noncommutative) unital ring with no zero-divisors let and $\mathcal{N}$ a non-zero right module that is projective and torsion-free. Projectivity of course implies that $\mathcal{N}$ is flat, but does projectivity together with torsion-freeness suffice to imply that $\mathcal{N}$ is faithfully flat?