consider a vertical piston system. the piston has a 50g mass and a given radius of 3mm. what amount of pressure does the piston exert? ( use g==9.8 m/s^2 )
Well, well, well, it seems we have a piston wanting to show off its pressure! Let's calculate that, shall we?
First, we need to determine the force the piston generates. We can use the equation:
Force = mass * acceleration
The mass of the piston is given as 50g, but we need to convert it to kilograms because 50g is barely enough to bother an ant! So, 50g = 0.05kg.
Now, to calculate the force, we have:
Force = 0.05kg * 9.8 m/s^2
Plugging the numbers in:
Force = 0.49 N
Alright, we have the force, but we need to find the pressure. The formula for pressure is:
Pressure = Force / Area
We still need to calculate the area, which is determined by the radius. The radius given is 3mm, but again, let's convert that to meters, because we like to keep things in the same units. So, 3mm = 0.003m.
The formula for the area of a circle is:
Area = π * radius^2
Plugging in the numbers:
Area = 3.14 * (0.003m)^2
Area = 3.14 * 0.000009m^2
Area = 0.00002826m^2
Now, we can find the pressure:
Pressure = 0.49 N / 0.00002826m^2
Pressure ≈ 17305.99 Pa
So, the piston exerts a whopping pressure of approximately 17305.99 Pascal. Don't be too impressed though, it's just doing its job!
To calculate the pressure exerted by the piston, we need to know the force exerted by the piston and the area over which the force is distributed.
Step 1: Calculate the force exerted by the vertical piston system.
The force exerted by the piston is equal to the mass of the piston multiplied by the acceleration due to gravity.
Given:
Mass (m) = 50 grams = 0.05 kg (since 1 kg = 1000 grams)
Acceleration due to gravity (g) = 9.8 m/s^2
Force (F) = m * g
F = 0.05 kg * 9.8 m/s^2
F = 0.49 N
Step 2: Calculate the area over which the force is distributed.
Given radius (r) = 3 mm = 0.003 m (since 1 m = 1000 mm)
Area (A) = π * r^2
A = π * (0.003 m)^2
A = 0.02827 m^2
Step 3: Calculate the pressure exerted by the piston.
Pressure (P) = Force (F) / Area (A)
P = 0.49 N / 0.02827 m^2
P = 17.3 Pa (rounded to one decimal place)
Therefore, the piston exerts a pressure of approximately 17.3 Pascal (Pa).
To calculate the amount of pressure exerted by the piston, you can use the formula:
Pressure = Force / Area
In this case, the force can be calculated using the mass of the piston and the acceleration due to gravity. The area can be calculated using the radius of the piston. Let's break down the steps to find the pressure:
Step 1: Calculate the force:
Force = Mass * Acceleration due to gravity
Force = 50g * 9.8 m/s^2 (as given in the question)
Step 2: Convert the mass to kilograms:
Given that 1 kg = 1000 g, we can convert the mass of the piston in grams to kilograms:
Mass = 50g / 1000 = 0.05 kg
Step 3: Calculate the area:
Area = π * (radius)^2
Area = π * (0.003m)^2 (radius is given in millimeters, so we need to convert it to meters)
Step 4: Calculate the pressure:
Pressure = Force / Area
Pressure = (0.05 kg * 9.8 m/s^2) / (π * (0.003m)^2)
Now, let's calculate the pressure using these values:
Pressure = (0.05 * 9.8) / (3.14 * (0.003)^2) ≈ 559,211.45 Pascal (Pa)
Therefore, the piston exerts approximately 559,211.45 Pascal of pressure.
m g /area
m = .050 KG
g = 9.8 m/s^2
area = pi r^2 = pi (9 *10^-6) meters^2
so
p = .0173 * 10^6 N/m^2 or Pascals
= 1.73 * 10^4 Pascals
or around .2 atmospheres