How Do You Calculate Area and Uncertainty for a Rectangular Plate?

[potermic]

I am not to sure how to calculate this out

A rectangular plate has a length of 23.2 +/- .2 cm and a width of 9.0 +/- .1 cm. calculate the area and its uncertainty

Anyhelp would be greatly apriciated

 

[Shooting Star]

It's best to have a look at http://physicsed.buffalostate.edu/pubs/MeasurementAnalysis/MA1_9ed.pdf" . Both give explicit examples of your type of problem, but use different methods. I think the first one is the simpler.

 

[Moetasim]

Dimensional analysis is a method used to convert units and solve problems involving different units of measurement. In this case, we are trying to calculate the area of a rectangular plate with given uncertainties in its length and width. To solve this problem, we can use the formula for area of a rectangle, which is length multiplied by width.

First, we need to identify the units for length and width. In this case, the length is given in centimeters (cm) and the width is also given in centimeters (cm). Since area is calculated by multiplying two quantities, the units for area will be cm^2 (square centimeters).

Next, we need to calculate the area using the given dimensions. We can use the following formula:

Area = length x width

Plugging in the given values, we get:

Area = (23.2 cm +/- .2 cm) x (9.0 cm +/- .1 cm)

To calculate the area with uncertainties, we need to use the rules of uncertainty propagation. Since we are multiplying two quantities, the uncertainties will be added. This means:

Area = (23.2 cm + .2 cm) x (9.0 cm + .1 cm)

= (23.4 cm) x (9.1 cm)

= 212.94 cm^2

Therefore, the area of the rectangular plate is 212.94 cm^2 with an uncertainty of +/- .3 cm^2. This means the final answer can be written as:

Area = 212.94 +/- .3 cm^2

I hope this helps you with your dimensional analysis problem. If you have any further questions, please don't hesitate to ask for more clarification.