Pressure exerted by 1 leg of a chair.

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In summary, a chair leg with a radius of 1 mm and a weight of 64 kg will exert a pressure of 5.2 x 10-7 cm2 on a hardwood floor.
  • #1
bfusco
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1

Homework Statement


Estimate the pressure exerted on a floor by one pointed chair leg (64kg on all four legs) of area = 3.0×10−2 cm^2.

The Attempt at a Solution


first i found the weight of the chair (mg) to be 627.2 N, and the weight on 1 leg is 1/4th of that, so the weight on one leg is 156.8 N. then i convert .03x10^-2 cm^2 to m^2 by dividing by 10000 to get 3x10^-6. Since pressure is =F/A , i take 156.8/3x10^-6 to get 5.2x10^7 or 52,266,666 which i have a hard time believing is correct.
 
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  • #2
Go back over your arithmetic. I think you have an error in what you have laid out here.
 
  • #3
OldEngr63 said:
Go back over your arithmetic. I think you have an error in what you have laid out here.

well i did see that i typed the given area of the bottom of the chair leg wrong while i was describing what i did thus far, but aside from that the conversion from cm^2 to m^2 seems correct to me (3x10^-2 → 3x10^-6). unless my method for coverting was done incorrectly.
 
  • #4
bfusco said:

Homework Statement


Estimate the pressure exerted on a floor by one pointed chair leg (64kg on all four legs) of area = 3.0×10−2 cm^2.

The Attempt at a Solution


first i found the weight of the chair (mg) to be 627.2 N, and the weight on 1 leg is 1/4th of that, so the weight on one leg is 156.8 N. then i convert .03x10^-2 cm^2 to m^2 by dividing by 10000 to get 3x10^-6. Since pressure is =F/A , i take 156.8/3x10^-6 to get 5.2x10^7 or 52,266,666 which i have a hard time believing is correct.

Your result looks okay; After all, these are rather sharp chair legs! With a cross sectional area of 3 x 10-2 cm2, if they're circular then their radius is about 1 mm. The hardwood floors would sure take a beating!
 
  • #5


I would like to first commend you for attempting to solve this problem and breaking it down into smaller steps. Your approach is correct, however, there are some minor errors in your calculations.

Firstly, the weight of the chair should be expressed in kilograms (kg) rather than Newtons (N). This is because weight is a force and it is measured in Newtons, but mass is measured in kilograms. So, the weight of the chair would be 64 kg, not 627.2 N.

Next, when finding the weight on one leg, you correctly divided the weight of the chair by 4, but you forgot to convert it to Newtons. So, the weight on one leg would be 15.2 N, not 156.8 N.

For the area, you correctly converted from cm^2 to m^2, but you forgot to take into account the units when dividing by 10,000. So, the area would be 3x10^-6 m^2, not 3x10^-6.

Finally, when calculating pressure, you correctly used the formula P=F/A, but you made a small error in your calculation. The pressure should be 5.2x10^4 Pa, not 5.2x10^7 Pa.

In conclusion, the pressure exerted by one leg of the chair on the floor would be 5.2x10^4 Pa, or 52,266 Pa, which is a reasonable value for the weight of a chair. Keep up the good work in problem solving and make sure to double check your calculations to avoid small errors.
 

Related to Pressure exerted by 1 leg of a chair.

1. What is the unit of measurement for pressure exerted by one leg of a chair?

The unit of measurement for pressure is force per unit area, typically expressed in pascals (Pa) or pounds per square inch (psi).

2. How is the pressure exerted by one leg of a chair calculated?

The pressure exerted by one leg of a chair is calculated by dividing the weight of the object, in this case the chair, by the surface area of the leg in contact with the ground.

3. Does the material of the leg affect the pressure it exerts?

Yes, the material of the leg does affect the pressure it exerts. Materials with a larger surface area, such as wide wooden legs, will distribute the weight of the chair over a larger area, resulting in less pressure. Materials with a smaller surface area, such as thin metal legs, will exert more pressure.

4. How does the weight of the person sitting in the chair affect the pressure exerted by one leg?

The weight of the person sitting in the chair will increase the overall weight of the object, resulting in more pressure being exerted by each leg. This is why chairs with a weight limit are important, as exceeding the weight limit can put too much pressure on the legs and cause them to break.

5. Can the pressure exerted by one leg of a chair be reduced?

Yes, the pressure exerted by one leg of a chair can be reduced by increasing the surface area of the leg, such as by adding a wider base or using a material with a larger surface area. Additionally, using multiple legs or distributing the weight of the chair over a larger area, such as by using a chair mat, can also help reduce pressure on each individual leg.

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