Question

A 6 N force is applied to the plunger of a hypodermic needle. The radius of the plunger is 0.40 cm and the radius of the needle is 0.010 cm. With what magnitude of force_out does the fluid leave the needle with respect to the force_in ?

Answer 1

Answer:

The magnitude of force the fluid leaves the needle is 3.75 x 10⁻³ N

Explanation:

Given;

applied force to the plunger, F = 6 N

radius of the plunger, r = 0.40 cm = 4 x 10⁻³ m

radius of the needle, r =  0.010 cm = 1 x 10⁻⁴ m

Pressure of the fluid is given as;

P = F / A

where;

A is area, = πr²

$P = \frac{F_{plunger}}{\pi r_{plunger}^2} = \frac{F_{needle}}{\pi r_{needle}^2}$

if pressure of the fluid is constant, the force applied to the plunger and force the fluid leaves the needle is given as;

$F_{needle} = \frac{F_{plunger}*r_{needle}^2}{r_{plunger}^2} \\\\F_{needle} = \frac{6 *(1*10^{-4})^2 }{(4*10^{-3})^2} = 3.75*10^{-3}\ N$

Therefore, the magnitude of force the fluid leaves the needle is 3.75 x 10⁻³ N