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 = 2.20 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 2.05 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. m/s

Question

Physics

Vance Raymond

23 December, 02:52

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 = 2.20 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 2.05 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. m/s

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Casey Cruz · Answer 1

13.65 m/s

Explanation:

Taken the speed of the liquid in the syringe to zero and using Bernoulli's principle

ΔP (change in pressure) = Force applied / area = 2.05 N / 2.20 * 10 ⁻⁵ m² = 93181.82 N / m²

ΔP = 1/2 ρv² where v is the speed of medicine at the mouth of the syringe and rho is density of water which 1000 kg/m³

93181.82 N / m² = 0.5 * 1000 * v²

v² = (93181.82 N / m²) / (0.5 * 1000) = 13.65 m/s