Answer
See answers.
Work Step by Step
a. The fluid is confined and the pressures are equal. Apply Pascal’s principle.
$$\frac{F_{plunger}}{A_{plunger}}=\frac{F_{needle}}{A_{needle}}$$
$$ F_{needle}=F_{plunger} \frac{A_{needle}}{A_{plunger}}$$
$$ F_{needle}=(3.2\;N) \frac{\pi (0.10\times10^{-3}m)^2}{\pi (0.65\times10^{-2}m)^2}=7.6\times 10^{-4}\;N$$
b. Find the plunger force.
$$F_{plunger}=P_{plunger}A_{plunger}=(75\;mm-Hg)(\frac{133\;N/m^2}{1\;mm-Hg})\pi(0.65\times10^{-2}m)^2=1.3\;N $$