# Biophysics Problem 29

A nurse wants to inject \(2\; g\) of polio vaccine into a student. With what average force must she push on the plunger if the speed of the vaccine coming out is \(1 \;m /s\) and the length of the plunger's motion in the syringe is \(6 \;cm\) (friction is ignored)?

Work done on the plunger equals the increase of energy of the fluid. Assume the potential energy does not change. Then, the increase of energy will be the increase of kinetic energy of the fluid. Since the fluid starts from rest, its initial kinetic energy will be the total change of energy.

Work done on the plunger will be

\(W = (F \times 0.06 \;m) J\)

What is the force in Newtons?

You should have:

\(F \times s = m\; v^2 / 2 \\ F = m\; v^2 / (2 \;s) \\ F = (0.002 \;kg) (1 \;m/s)^2 / (2 (0.06\; m)) \\ F = 0.0167\;N\)