michelle weighs 900 N. How much pressure does she apply when she stands on her head, if the part of her head touching the floor has a radius of 2cm?
To calculate the pressure exerted by Michelle when she stands on her head, you need to apply the formula:
Pressure = Force / Area
First, convert the weight of Michelle from Newtons (N) to kilograms (kg). Since the acceleration due to gravity is approximately 9.8 m/s², the weight in kilograms can be determined by dividing the weight in Newtons by the acceleration due to gravity (9.8 m/s²):
Weight in kg = Weight in N / Acceleration due to gravity
Weight in kg = 900 N / 9.8 m/s²
Next, calculate the area of the part of her head touching the floor. Since it is given that the radius is 2 cm, you need to convert it to meters by dividing by 100:
Radius in meters = Radius in cm / 100
Radius in meters = 2 cm / 100
Then, calculate the area of the circle using the formula:
Area = π * Radius²
Area = π * (Radius in meters)²
Now, you can substitute the weight in kg and the area into the pressure formula:
Pressure = Weight in kg / Area
Finally, calculate the pressure:
Pressure = Weight in kg / Area
Note: Ensure that the units of weight and area are consistent; if not, convert them as necessary.
So, by following these steps, you can calculate the pressure Michelle applies on the floor when she stands on her head.