A nurse needs to inject liquid medicine into your body by exerting a 2N force onto a hypodermic syringe. If the crossectional area of the barrel of the syringe is 0.05 m2 and the syringe's needle is 0.0025 m2, with how many newtons of force does the medicine come out from the needle into your body? What principle do you use in this problem? 1.0 N, Achemides principal 0.1N, Bernoulli principal 0.1 N, Pascal principal 0.005N, Pascal principal
Question
A nurse needs to inject liquid medicine into your body by exerting a 2N force onto a hypodermic syringe. If the crossectional area of the barrel of the syringe is 0.05 m2 and the syringe's needle is 0.0025 m2, with how many newtons of force does the medicine come out from the needle into your body? What principle do you use in this problem? 1.0 N, Achemides principal 0.1N, Bernoulli principal 0.1 N, Pascal principal 0.005N, Pascal principal
Solution
The correct answer is "0.1 N, Pascal principle".
Here's the step-by-step solution:
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The principle used in this problem is Pascal's principle. Pascal's principle states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.
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According to Pascal's principle, the pressure applied to the fluid in the syringe will be the same throughout the fluid. Pressure is defined as force divided by area. So, the pressure applied by the nurse is 2N / 0.05 m2 = 40 N/m2.
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This same pressure is exerted on the fluid as it exits the needle. So, we can find the force with which the medicine comes out of the needle by rearranging the pressure equation to solve for force (Force = Pressure x Area).
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Substituting the values, we get Force = 40 N/m2 x 0.0025 m2 = 0.1 N.
So, the medicine comes out from the needle into your body with a force of 0.1 N.
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