Using moments to calculate weight of Pyrometer stand base

[Purplepixie]

I am trying to design a free standing stand for a pyrometer, which weighs 750g. The pyrometer needs to be 1.5 metres above ground level. The stand will be constructed entirely in steel. The layout of the stand is shown in the uploaded diagram Pyro_stand.gif. How can I derive expressions for the minimum required weight of the stand base (ie any lower weight will result in the pyrometer & stand tipping over), in terms of the variables shown in the diagram ? All distances are in centimetres, and weights are in grams. Many thanks in advance!

 

[jvicens]

Hello,

Firstly, to determine the minimum required weight of the stand base, we need to consider the forces acting on the pyrometer and stand. These forces include the weight of the pyrometer itself, the weight of the stand, and any external forces such as wind or vibrations.

To prevent the pyrometer and stand from tipping over, we need to ensure that the center of mass of the entire system (pyrometer + stand) is located within the base of the stand. This means that the weight of the base needs to be greater than or equal to the weight of the pyrometer and stand combined.

To calculate the weight of the pyrometer and stand combined, we can use the formula:

Weight = Mass x Gravity

Since the mass of the pyrometer is given as 750g, we can calculate its weight as:

Wpyro = 750g x 9.8 m/s^2 = 7350 g·m/s^2

Next, we need to consider the weight of the stand. The stand is constructed entirely in steel, so we can assume that it has a uniform density and can be treated as a solid object. The weight of the stand can be calculated using the formula:

Wstand = Volume x Density x Gravity

The volume of the stand can be calculated as the product of its length, width, and height:

Vstand = L x W x H = 30cm x 30cm x 150cm = 135,000 cm^3

The density of steel is approximately 7.85 g/cm^3, so the weight of the stand can be calculated as:

Wstand = 135,000 cm^3 x 7.85 g/cm^3 x 9.8 m/s^2 = 10,523,500 g·m/s^2

Therefore, the total weight of the pyrometer and stand combined is:

Wtotal = Wpyro + Wstand = 7350 g·m/s^2 + 10,523,500 g·m/s^2 = 10,524,850 g·m/s^2

To ensure that the center of mass of the system is within the base of the stand, the weight of the base needs to be greater than or equal to the total weight of the pyrometer and stand combined. Therefore, the minimum required weight of the stand base can be expressed as:

Wbase ≥ Wtotal = 10,524,