How Do Uncertainties Affect Calculations in Cookie Volume and Size Ratios?

In summary, the cookies in the bag have a diameter of 8.50+-0.02cm and a thickness of 0.050+-0.005cm. Using these measurements, the average volume of a cookie is 2.8+-0.3cm and the ratio of the diameter to the thickness is 170+-20cm. Different methods can be used to find these values, such as using extreme values and the middle value to determine the range of the volume and ratio.
  • #1
iampaul
93
0

Homework Statement


As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50+-0.02cm and a thickness of 0.050+-0.005cm.


Homework Equations


a. Find the average volume of of a cookie and the uncertainty in the volume.
b.Find the ratio of the diameter to the thickness and the uncertainty in the ratio.


The Attempt at a Solution


The answer for a is 2.8+-0.3cm
The answer for b is 170+-20cm
Can someone please show how . Thanks.
 
Physics news on Phys.org
  • #2
iampaul said:

Homework Statement


As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50+-0.02cm and a thickness of 0.050+-0.005cm.

Homework Equations


a. Find the average volume of of a cookie and the uncertainty in the volume.
b.Find the ratio of the diameter to the thickness and the uncertainty in the ratio.

The Attempt at a Solution


The answer for a is 2.8+-0.3cm
The answer for b is 170+-20cm
Can someone please show how . Thanks.

(a) One way is to use extreme values of diameter and thickness, as well as the middle value to get the middle value and extremes of volume, then see what range is needed to cover the answers.

ie for mean: d= 8.50, th = 0.050

Upper d = 8.52 th = 0.055

Lower d = 8.48 th = 0.450

(b) you can sort of do the same thing, but must be careful that you don't alwys get the upper limit by making all values as big as possible, and similarly smallest doesn't mean all small. [this time you are using the d:th ratio of course. In part (a) you finding the volume
 

Related to How Do Uncertainties Affect Calculations in Cookie Volume and Size Ratios?

1. What is the concept of uncertainty in physics?

Uncertainty in physics refers to the lack of precise knowledge or measurement in a physical quantity. It is the degree of doubt or error associated with a measurement or calculation.

2. How is uncertainty calculated in physics?

Uncertainty is typically calculated by taking the difference between the measured value and the accepted or expected value, and dividing it by the accepted value. This result is then multiplied by 100 to get a percentage value.

3. What are some sources of uncertainty in physics experiments?

There are several sources of uncertainty in physics experiments, including limitations of measuring instruments, human error in taking measurements, and inherent variability in physical systems. Environmental factors such as temperature and pressure can also contribute to uncertainty.

4. How does uncertainty affect the results of a physics experiment?

Uncertainty can affect the accuracy and precision of the results of a physics experiment. A high level of uncertainty means that the results may not be reliable or may have a large margin of error. It is important to minimize uncertainty in order to obtain more accurate and precise measurements.

5. How can uncertainty be reduced in physics experiments?

Uncertainty can be reduced by using more precise measuring instruments, taking multiple measurements and averaging them, and controlling environmental factors that may affect the experiment. It is also important to follow proper experimental procedures and minimize human error in taking measurements.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
9K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
27K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Precalculus Mathematics Homework Help
Replies
18
Views
8K
Replies
2
Views
2K
Replies
7
Views
5K
Back
Top