Help on Physics problem?

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A 4.00 mL syringe has an inner diameter of 5.00 mm , a needle inner diameter of 0.210 mm , and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient whose blood pressure is 140/100.

Part A:What is the minimum force the nurse needs to apply to the syringe?

Part B: The nurse empties the syringe in 4.40 s . What is the flow speed of the medicine through the needle?

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1 Answer

  • A/

    blood pressure

    p = 140mmHg * 1.01e5Pa / 760mmHg = 18665 Pa

    force against end of syringe

    F = p*A = 18665Pa * π(0.00500m)²/4 = 0.366 N

    B/

    Q = V / t = 4.00mL / 4.40s = 0.909 mL/s = 0.909 cm³/s

    Then velocity

    v = Q / A = 0.909cm³/s / (π(0.0210cm)²/4) = 2620 cm/s

    or 26.2 m/s

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