Pressure Exerted on Floor

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In summary, the pressure is 263.25 N/cm^2 on the heel of a high-heeled shoe when the woman is standing on the Earth's surface.
  • #1
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Homework Statement



A 41.1-kg woman balances on one heel of a pair of high-heeled shoes. If the heel is circular and has a radius of 0.698 cm, what pressure does she exert on the floor?


2. The attempt at a solution

Pressure is a force applied over an area. The woman has a weight (force) which is related to her mass and gravity. Since we're not told different, we'll assume she's standing on the surface of the Earth, where the acceleration of gravity is 9.8 m/s^2. So, her weight is

W = 41.1 kg * 9.8 m/s^2 = 402.78

Since she's balancing on the heel of one shoe, all her weight is applied over that area. The area is related to the radius by the familiar formula from geometry class,

A = pi * r^2
A = 3.14 * (0.698 cm)^2
A = 1.53 cm^2

So, the pressure is

P = W / A
P = 402.78 N / 1.53 cm^2
P = 263.25 N/cm^2


But it says incorrect. Did I mess up somewhere? Please help.
 
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  • #2
mparsons06 said:

Homework Statement



A 41.1-kg woman balances on one heel of a pair of high-heeled shoes. If the heel is circular and has a radius of 0.698 cm, what pressure does she exert on the floor?


2. The attempt at a solution

Pressure is a force applied over an area. The woman has a weight (force) which is related to her mass and gravity. Since we're not told different, we'll assume she's standing on the surface of the Earth, where the acceleration of gravity is 9.8 m/s^2. So, her weight is

W = 41.1 kg * 9.8 m/s^2 = 402.78

Since she's balancing on the heel of one shoe, all her weight is applied over that area. The area is related to the radius by the familiar formula from geometry class,

A = pi * r^2
A = 3.14 * (0.698 cm)^2
A = 1.53 cm^2

So, the pressure is

P = W / A
P = 402.78 N / 1.53 cm^2
P = 263.25 N/cm^2


But it says incorrect. Did I mess up somewhere? Please help.

Are you sure that "it" has the same units as you? That might be a good place to start looking...
 
  • #3
Thanks! It was actually N/m^2.
 

1. What is pressure exerted on floor?

Pressure exerted on floor is the force applied by an object on the surface of the floor. It is calculated by dividing the force by the area over which the force is distributed.

2. How is pressure exerted on floor measured?

Pressure exerted on floor is measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m^2).

3. What factors affect the pressure exerted on floor?

The pressure exerted on floor is affected by the weight of the object, the size of the area over which the weight is distributed, and the type of surface the object is resting on.

4. How does pressure exerted on floor impact the floor itself?

High pressure exerted on floor can lead to damage or deformation of the floor, especially if it is not strong enough to support the weight. It can also cause sinking or sinking of the floor in areas with weaker foundations.

5. How can pressure exerted on floor be reduced?

To reduce the pressure exerted on floor, the weight of the object can be distributed over a larger area, or a stronger surface can be used to support the object. Another way to reduce pressure is to decrease the weight of the object itself.

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