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

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Now, let's delve into the physics behind this scenario. When the 50 kg girl stands on a single heel with a circular shape and a diameter of 1.0 cm, we need to calculate the pressure exerted by the heel on the floor.

Pressure, in physics, is defined as force per unit area. We can calculate it using the formula:

Pressure=ForceAreaPressure=AreaForce

In this case, the force exerted by the girl standing on the heel is equal to her weight, which is 50 kg multiplied by the acceleration due to gravity (9.8 m/s²). So, the force (F) exerted by the girl is:

F=m×gF=m×g F=50 kg×9.8 m/s2F=50kg×9.8m/s2 F=490 NF=490N

Now, to find the area of the circular heel, we'll use the formula for the area of a circle:

Area=π×(diameter2)2Area=π×(2diameter)2 Area=π×(1.0 cm2)2Area=π×(21.0cm)2 Area=π×0.52 cm2Area=π×0.52cm2 Area=π×0.25 cm2Area=π×0.25cm2 Area≈0.785 cm2Area≈0.785cm2

Now, we can calculate the pressure:

Pressure=490 N0.785 cm2Pressure=0.785cm2490N

This gives us the pressure exerted by the heel on the horizontal floor. However, it's essential to note that we need to convert the area to square meters to match the unit of force (Newtons) to obtain the pressure in Pascals (Pa).

0.785 cm2=0.0000785 m20.785cm2=0.0000785m2

Now, let's calculate the pressure:

Pressure=490 N0.0000785 m2Pressure=0.0000785m2490N Pressure≈6,242,038 PaPressure≈6,242,038Pa

So, the pressure exerted by the heel on the horizontal floor is approximately 6,242,038 Pascals.

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