Pressure exerted by 1 leg of a chair.

[bfusco]

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.

 

[OldEngr63]

Go back over your arithmetic. I think you have an error in what you have laid out here.

 

[bfusco]

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.

 

[gneill]

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!

 

[asteriatic]

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.