A full term fetus may have a mass of 3.3 kg . If the entire weight of the fetus rests momentarily on the mother's bladder, supported on an area of 78.8 cm2 calculate the pressure exerted in mmHg.
To calculate the pressure exerted by the fetus on the mother's bladder, we can use the formula:
Pressure = Force / Area
First, we need to convert the mass of the fetus from kg to grams since pressure is typically calculated using SI units.
Given:
Mass of the fetus = 3.3 kg
Converting kg to grams:
1 kg = 1000 grams
So, the mass of the fetus in grams = 3.3 kg * 1000 grams/kg = 3300 grams
Next, we need to calculate the force exerted by the fetus on the mother's bladder. We can use the equation:
Force = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Given:
Mass of the fetus = 3300 grams
Force = 3300 grams * 9.8 m/s^2
Now, we have the force exerted by the fetus in grams * m/s^2. However, we need to convert this to newtons (N) since pressure is typically calculated using SI units.
1 g * m/s^2 = 0.0098 N
So, the force exerted by the fetus = (3300 grams * 9.8 m/s^2) * 0.0098 N/(g * m/s^2)
Next, we need to convert the area from cm^2 to m^2.
Given:
Area = 78.8 cm^2
1 cm^2 = (0.01 m)^2 = 0.0001 m^2
So, the area in m^2 = 78.8 cm^2 * 0.0001 m^2/cm^2
Now that we have the force and the area in proper units, we can calculate the pressure.
Pressure = Force / Area
= (force in N) / (area in m^2)
Finally, we need to convert the resulting pressure to mmHg.
1 N/m^2 = 0.00750062 mmHg
So, the pressure exerted by the fetus in mmHg = (pressure in N/m^2) * 0.00750062 mmHg/(N/m^2)
Follow these steps using the given values to calculate the pressure exerted by the fetus on the mother's bladder in mmHg.
To calculate the pressure exerted in mmHg, we need to use the formula:
Pressure (P) = Force (F) / Area (A)
First, we need to convert the mass of the fetus from kilograms to grams, as the units of weight in the formula should be consistent with the units of force used. Since 1 kilogram is equal to 1000 grams, the mass of the fetus in grams will be:
Mass of fetus = 3.3 kg * 1000 g/kg = 3300 g
Now, to calculate the force exerted by the fetus, we can use the equation:
Force = Mass * acceleration due to gravity
where the standard value for acceleration due to gravity is approximately 9.8 m/s².
Force = 3300 g * 9.8 m/s²
Next, we need to convert the area from cm² to m², as the units of area in the formula should also be consistent. Since 1 cm² is equal to 0.0001 m², the area in m² will be:
Area = 78.8 cm² * 0.0001 m²/cm² = 0.00788 m²
Now, we can substitute the values into the formula to calculate the pressure:
Pressure (P) = Force (F) / Area (A)
Pressure = (3300 g * 9.8 m/s²) / 0.00788 m²
Simplifying further:
Pressure = 32400 g·m/s² / 0.00788 m²
Lastly, to convert the pressure to mmHg, we use the conversion factor: 1 mmHg = 133.322 Pa (Pascal).
Pressure = (32400 g·m/s² / 0.00788 m²) * (1 mmHg / 133.322 Pa)
Therefore, the pressure exerted in mmHg when the entire weight of the 3.3 kg fetus rests momentarily on an area of 78.8 cm² will be calculated using the above steps.