A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with the diameter 1.0 cm. What is the pressure exerted on the horizontal floor in MPa

To find the pressure exerted on the horizontal floor, we can use the formula:

Pressure = Force / Area

First, let's calculate the force exerted by the girl on the floor. The force can be calculated using the formula:

Force = mass * gravity

where the mass of the girl is 50 kg and the acceleration due to gravity is approximately 9.8 m/s^2.

Force = 50 kg * 9.8 m/s^2 Force = 490 N

Next, we need to calculate the area of the circular heel. The area of a circle can be calculated using the formula:

Area = π * (radius)^2

The radius of the heel can be found by dividing the diameter by 2:

Radius = 1.0 cm / 2 Radius = 0.5 cm

Now, we convert the radius to meters:

Radius = 0.5 cm * 0.01 m/cm Radius = 0.005 m

Using this radius, we can calculate the area:

Area = π * (0.005 m)^2 Area = 0.00007854 m^2

Finally, we can calculate the pressure:

Pressure = Force / Area Pressure = 490 N / 0.00007854 m^2 Pressure = 6,235,294.12 Pa

To convert the pressure to MPa, we divide by 1,000,000:

Pressure = 6,235,294.12 Pa / 1,000,000 Pressure = 6.235 MPa

Therefore, the pressure exerted on the horizontal floor by the girl wearing high heel shoes is approximately 6.235 MPa.