A syringe has an area of 1.4 cm2 at its barrel and then narrows down to an area of 0.11 mm2 at the needle end. If a force of 4.7 N is applied to the syringe, what is the force produced at the tip of the needle?
To solve this problem, we can use the principle of Pascal's law, which states that the pressure applied to a fluid in a closed system is transmitted equally in all directions.
First, let's calculate the pressure applied to the syringe. Pressure is defined as force divided by area. Thus, the pressure applied to the syringe is:
Pressure_syringe = Force / Area_syringe
Substituting the given values, we have:
Pressure_syringe = 4.7 N / 1.4 cm^2
However, to make calculations easier, let's convert the areas to the same unit first. 1 cm^2 is equal to 100 mm^2. Therefore:
Area_syringe = 1.4 cm^2 = 1.4 * 100 mm^2 = 140 mm^2
Substituting the new value for area, we have:
Pressure_syringe = 4.7 N / 140 mm^2
Now, we need to calculate the force produced at the tip of the needle. Since the pressure is transmitted equally in all directions, the pressure at the tip of the needle will be the same as the pressure in the syringe.
Using the principle of Pascal's law again, we can now find the force at the tip of the needle:
Force_needle = Pressure_syringe * Area_needle
Substituting the values, we have:
Force_needle = Pressure_syringe * 0.11 mm^2
Thus, the force produced at the tip of the needle is equal to the calculated value.