  We investigate polymer translocation through a nanopore under a pulling force
using Langevin dynamics simulations. We concentrate on the influence of the
chain length $N$ and the pulling force $F$ on the translocation time $\tau$.
The distribution of $\tau$ is symmetric and narrow for strong $F$. We find that
$\tau\sim N^{2}$ and translocation velocity $v\sim N^{-1}$ for both moderate
and strong $F$. For infinitely wide pores, three regimes are observed for
$\tau$ as a function of $F$. With increasing $F$, $\tau$ is independent of $F$
for weak $F$, and then $\tau\sim F^{-2+\nu^{-1}}$ for moderate $F$, where $\nu$
is the Flory exponent, which finally crosses over to $\tau\sim F^{-1}$ for
strong force. For narrow pores, even for moderate force $\tau\sim F^{-1}$.
Finally, the waiting time, for monomer $s$ and monomer $s+1$ to exit the pore,
has a maximum for $s$ close to the end of the chain, in contrast to the case
where polymer is driven by an external force within the pore.
