Read the activity 2-1:Force and Pressure in the lab manual (pages 167-168). As described in the manual, consider a 10 cc syringe is connected to a 50 cc syringe. Information of the syringes are as follows:
(mass of 10 cc piston) = 16 g
(mass of 50 cc piston) = 60.6 g
(diameter of 10 cc piston) = 14.7 mm
(diameter of 50 cc piston) = 28.0 mm.
If a force probe is attached to the 50 cc piston, what do you expect will be the force measurement while a 50 g mass is placed on the 10 cc piston?
(d) Now, the 50 g mass is removed from the 10 cc piston, and another force probe is attached to the 10 cc piston. Now both 10 cc piston and 50 cc piston have force probes attached to them. Consider that the 10 cc piston is pressed down with a force FA, and let's call FB to be the force measured by the force probe on the 50 cc piston. If you write FA as a function of FB, what is the slope of the function?
To answer this question, we first need to understand the relationship between force and pressure in a syringe.
Force (F) and pressure (P) are related by the equation:
F = P * A
where F is the force, P is the pressure, and A is the cross-sectional area of the piston.
In the first part of the question, the 10 cc syringe is connected to the 50 cc syringe, and a force probe is attached to the 50 cc piston. We are given the following information:
Mass of 10 cc piston (m1) = 16 g
Mass of 50 cc piston (m2) = 60.6 g
Diameter of 10 cc piston (d1) = 14.7 mm
Diameter of 50 cc piston (d2) = 28.0 mm
To find the force measurement when a 50 g mass is placed on the 10 cc piston, we can calculate the pressure exerted on the 50 cc piston.
First, we need to find the area of both pistons.
Area of 10 cc piston (A1) = π * (d1/2)^2
Area of 50 cc piston (A2) = π * (d2/2)^2
Now, we can calculate the pressure on the 50 cc piston when a 50 g mass is placed on the 10 cc piston.
Pressure (P2) = (mass on 10 cc piston)/(area of 10 cc piston)
= (50 g)/(A1)
= (50 g)/[π * (d1/2)^2]
Next, we can find the force exerted on the 50 cc piston using the calculated pressure.
Force (F2) = Pressure (P2) * Area of 50 cc piston
= P2 * A2
Now we can substitute the values we have:
Area of 10 cc piston (A1) = π * (14.7 mm/2)^2
Area of 50 cc piston (A2) = π * (28.0 mm/2)^2
Pressure (P2) = (50 g)/[π * (14.7 mm/2)^2]
Force (F2) = P2 * [π * (28.0 mm/2)^2]
By performing the calculations, we can find the force measurement (F2) when the 50 g mass is placed on the 10 cc piston.
Now, let's move on to the second part of the question.
In this part, the 50 g mass is removed from the 10 cc piston, and a force probe is attached to the 10 cc piston as well. Both the 10 cc piston and the 50 cc piston have force probes attached to them.
We are asked to write FA as a function of FB, where FA is the force measured by the force probe on the 10 cc piston, and FB is the force measured by the force probe on the 50 cc piston.
Since both the 10 cc and 50 cc pistons have force probes attached to them, the force exerted on each piston (FA and FB) will be the same. Thus, we can write:
FA = FB
Therefore, the slope of the function is 1.
To summarize:
- The force measurement on the 50 cc piston when a 50 g mass is placed on the 10 cc piston can be found by calculating the pressure on the 50 cc piston using the mass and the dimensions of the 10 cc piston and the area of the 50 cc piston.
- The force measurement on both the 10 cc piston and the 50 cc piston when the 50 g mass is removed can be considered equal, resulting in the equation FA = FB and a slope of 1.