Exerting a force of 94 N on the circular piston of a syringe causes a pressure increase in the barrel of 1.3 atm. What is the diameter of the piston?
P = 1.3 atm = 1.3*10^5 N/m^2
P = Force/Area = 94 N/A
Solve for the area A, and use that to get the diameter.
A = 94 N/(1.3*10^5 N/m^2)
= 7.23*10^-4 m^2
= 7.23 cm^2
Pi/4 d^2= A
To find the diameter of the piston, we can use the equation for pressure (P) in terms of force (F) and area (A):
P = F/A
We are given the force exerted on the circular piston (F = 94 N) and the pressure increase in the barrel (P = 1.3 atm). We need to find the diameter of the piston, which will allow us to calculate the area.
First, let's convert the pressure from atm to Pascals (Pa), since the SI unit for pressure is the Pascal:
1 atm = 101325 Pa
Therefore, the pressure in Pascals is:
P = 1.3 atm * 101325 Pa/atm = 132122.5 Pa
Now, we can rearrange the equation to solve for the area:
A = F/P
Plugging in the values:
A = 94 N / 132122.5 Pa ≈ 0.0007 m^2
The area of a circle is given by the formula:
A = π * (d/2)^2
where d is the diameter of the circular piston.
Rearranging the formula to solve for d:
d = √(4A/π)
Plugging in the value of A:
d = √(4 * 0.0007 m^2 / π) ≈ 0.118 m
Therefore, the diameter of the piston is approximately 0.118 meters.