A hypodermic needle consists of a plunger of circular cross-section that slides inside a hollow cylindrical syringe. When the plunger is pushed, the contents of the syringe are forced through a hollow needle (also of circular cross section). If a 4.0- N force is applied to the plunger and the diameters of the plunger and the needle are 1.2 cm and 2.5 mm, respectively, what force is needed to prevent fluid flow at the needle?
A)0.17N B)0.27N C)0.43N D)0.83N E)2.7N
plzz ineed help i have no idea what im supposed to do here!
The pressures are the same:
force1/area1=force2/area2
force1/diameter1^2=force2/diameter2^2
force2=force1*(diameter2/diameter1)^2
force1=4N*(.25cm/1.2cm)^2=.174N check that
thanks a lot i appreciate it
To solve this problem, you can use Pascal's Law, which states that the pressure applied to an enclosed fluid will be transmitted undiminished to all portions of the fluid and to the walls of its container.
First, we need to calculate the pressure exerted on the fluid by the plunger. We can use the formula for pressure:
Pressure = Force / Area
The area of the plunger is given by:
Area = π * (radius)^2 = π * (diameter / 2)^2
Given that the diameter of the plunger is 1.2 cm, the radius is 0.6 cm (or 0.006 m):
Area = 3.14 * (0.006)^2 = 0.000113 m^2
Now, we can calculate the pressure:
Pressure = 4.0 N / 0.000113 m^2 ≈ 35398.23 Pa
Since the pressure is transmitted undiminished through the fluid to the needle, we can apply the same pressure to the needle to prevent fluid flow. Now, we need to calculate the force required to prevent fluid flow at the needle.
The area of the needle is given by:
Area = π * (radius)^2 = π * (diameter / 2)^2
Given that the diameter of the needle is 2.5 mm, the radius is 1.25 mm (or 0.00125 m):
Area = 3.14 * (0.00125)^2 = 0.0000049087 m^2
To calculate the force required, we can rearrange the pressure formula:
Force = Pressure * Area
Force = 35398.23 Pa * 0.0000049087 m^2 ≈ 0.1737 N
Therefore, the force needed to prevent fluid flow at the needle is approximately 0.17 N.
Therefore, the correct answer is A) 0.17 N.
To solve this problem, we can use Pascal's law, which states that pressure applied to a fluid is transmitted equally in all directions.
First, let's convert the given diameters into radii. The radius of the plunger is 1.2 cm / 2 = 0.6 cm = 0.006 m. The radius of the needle is 2.5 mm / 2 = 1.25 mm = 0.00125 m.
Next, we can calculate the areas of the plunger and the needle. The area of a circle is given by the formula A = πr^2.
Area of the plunger (A_plunger) = π(0.006 m)^2
Area of the needle (A_needle) = π(0.00125 m)^2
Now, let's calculate the pressure exerted on the fluid in the syringe due to the applied force on the plunger. Pressure (P) is defined as force divided by area.
Pressure on the fluid in the syringe (P_plunger) = Force applied to the plunger / Area of the plunger
Substituting the given values and performing the calculation:
P_plunger = 4.0 N / [π(0.006 m)^2]
Now, since the pressure is transmitted equally in all directions, the pressure at the needle (P_needle) is the same as the pressure at the plunger.
P_needle = P_plunger = 4.0 N / [π(0.006 m)^2]
Finally, to find the force needed to prevent fluid flow at the needle, we can use the formula for pressure:
Pressure (P) = Force (F) / Area (A)
Rearranging the formula to solve for force:
Force (F) = Pressure (P) × Area (A)
Substituting the given values and performing the calculation:
Force needed to prevent fluid flow at the needle = P_needle × A_needle
Now, let's plug in the values and calculate the force needed:
Force needed = [4.0 N / [π(0.006 m)^2]] × [π(0.00125 m)^2]
Simplifying the expression:
Force needed = (4.0 N × 0.00125 m^2) / (0.006 m)^2
Force needed ≈ 0.2083 N
The force needed to prevent fluid flow at the needle is approximately 0.2083 N.
Since this value is not one of the answer choices given, it is possible that there may have been an error in the calculations or transcription of the problem. Please double-check the given values and the calculations to ensure accuracy.