A hypodermic syringe contains a medicine with the density of water (see figure below). The barrel of the syringe has a cross-sectional area A = 2.30 10-5 m2, and the needle has a cross-sectional area a = 1.00 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F with arrow of magnitude 3.02 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle’s tip.
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The pressure inside the syringe is
p = 3.02N / 2.30e-5m² = 139 130 Pa
By Bernoulli’s principle, and since the syringe is horizontal,
Δp = ½ρv²
139130 Pa = ½ * 1000kg/m³ v²
v = 16.7 m/s
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