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.

(a) What is the pressure exerted by the 10 cc piston onto the air underneath?
kPa

(b) If a 50 g mass is placed on the 10 cc piston, what is the pressure exerted by the 10 cc piston onto the air underneath?
kPa

(c) 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?
N

(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?


totally stumped help anyone?

ok so. I solved first part with F/A i got .9239 kPa.

second part i solved to i just added the forces. I got 3.811 kPa.

The last two i am having difficulty with....

So since i know F/A=F/A

I'm just confused on how it affects one another....

i tried 646.8/169.71=F2/615.752 and tried solving for F but i am getting 2346.759 and it just not right..

should not F2=F1*A2/A so F2=646.8*(615.752/169.71)

F2=2346.759

The important thing to remember is that the pressure is uniform throughout the fluid (air?), so that the ratio of piston weight (plus applied force) to piston area is the same on both sides (i.e., both syringes) . You seem to have grasped that already.

Lets take the small pisiont with its 50 g nass

.05g/PI(.0147)^2/4 = Forcereadin/PI(.027)^2/4

or

forcereading=.05g*(.027/.0147)^2

To solve these problems, we need to use the formulas related to force, pressure, and area. Let's break down each part of the question and explain how to calculate the answers.

(a) To calculate the pressure exerted by the 10 cc piston onto the air underneath, we need to use the formula P = F/A, where P is the pressure, F is the force, and A is the area. Since we are given the diameter of the 10 cc piston (14.7 mm), we can calculate the area using the formula A = π * (d/2)^2, where d is the diameter. In this case, the diameter is 14.7 mm, so the radius is (14.7 mm)/2 = 7.35 mm = 0.00735 m. Thus, the area is A = π * (0.00735 m)^2.

Given the mass of the 10 cc piston is 16 g, we can convert it to kilograms (kg) by dividing by 1000 (since 1 g = 0.001 kg). So, the mass in kilograms is (16 g)/1000 = 0.016 kg. We can now find the force exerted by the 10 cc piston using the formula F = m*g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, F = 0.016 kg * 9.8 m/s^2.

Lastly, we can substitute the calculated values into the formula P = F/A to find the pressure in kPa (kilopascals). Make sure to convert the force to Newtons (N) by multiplying it by 9.8 (since 1 kg * 9.8 m/s^2 = 9.8 N) before dividing by the area. The final answer will be in kPa.

(b) Similarly, we can use the same formula P = F/A to calculate the pressure exerted by the 10 cc piston onto the air underneath when a 50 g mass is placed on it. We already have the formula for force (F) from part (a), so we can use that. However, this time we need to account for the extra mass (50 g) by adding it to the original mass (16 g) and converting it to kilograms (kg). After finding the combined mass (m) in kilograms, we can calculate the force (F) using the formula F = m*g. Then, use the formula P = F/A to find the pressure in kPa.

(c) When a force probe is attached to the 50 cc piston, the force measurement will be equal to the weight exerted on it. In this case, a 50 g mass is placed on the 10 cc piston. So, the force measured by the force probe attached to the 50 cc piston will be equal to the weight of the 50 g mass. To convert the mass to force (F), multiply it by the acceleration due to gravity (g).

(d) To write FA as a function of FB, we can use the principle of Pascal's Law. According to Pascal's Law, the pressure in a fluid (in this case, the air) is transmitted equally in all directions. Thus, the pressure exerted by the 10 cc piston (P1) will be equal to the pressure exerted by the 50 cc piston (P2). We can represent this as P1 = P2.

Pressure is given by the formula P = F/A, where F is the force and A is the area. We know the area of both pistons (10 cc and 50 cc). So, we can rewrite the equation as F1/A1 = F2/A2. Since we are interested in knowing FA as a function of FB, we can rearrange the equation to solve for FA:

FA = (F2/A2) * A1.

Here, F2 represents the force measured by the force probe on the 50 cc piston, and A1 and A2 represent the areas of the 10 cc and 50 cc pistons, respectively. Therefore, the slope of the function relating FA to FB would be (A1/A2).

By following these steps, you should be able to calculate the answers to the given questions using the provided information about the syringes.