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.

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 ?

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Thanh Hà 3 years 2021-07-22T13:08:14+00:00 1 Answers 59 views 0

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  1. Nem
    0
    2021-07-22T13:09:44+00:00
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    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

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