'Reversing' a moments calculation

In summary: This will allow you to determine how the forces change when the position of the balancing force F is shifted. In summary, the position of the balancing force F can be determined by taking moments about F and using a system of equations to solve for the three unknown forces f1, f2, and f3.
  • #1
Beamy
3
0
[URL]http://homepage.ntlworld.com/russelliott/shifting-cofg-1.png[/URL]

A rigid weightless beam is supported on 3 springs, spaced as marked. The forces in the 3 springs are initially equal (at 10N). The position of the 30N balancing force F to keep the system in equilibrium is determined from taking moments about F:

f1x1 + f2x2 = f3x3
10(20 + x2) + 10x2 = 10(29 - x2) [substituting values, to isolate x2]
200 + 10x2 + 10x2 = 290 - 10x2 [expanding]
30x2 = 90
x2 = 3

So far so good.

Homework Statement



What I'm trying to determine is what happens to the spring forces f1, f2 and f3 if the position of the balancing force F is shifted, say a further short distance x4 to the right (and with F remaining at 30N):

[URL]http://homepage.ntlworld.com/russelliott/shifting-cofg-2.png[/URL]

Homework Equations


The Attempt at a Solution



From the second diagram I get a number of moment equations:

f1(23 + x4) + f2(3 + x4) = f3(26 - x4) [taking moments about F]
23f1 + f1x4 + 3f2 + f2x4 = 26f3 - f3x4 [expanded]
f1x4 + f2x4 + f3x4 = 26f3 - 23f1 - 3f2 [further expanded]
30x4 = 26f3 - 23f1 - 3f2 [given that f1 + f2 + f3 = F = 30]

30(23 + x4) = 20f2 + 49f3 [taking moments about f1]
30x4 = 20f2 + 49f3 - 690

20f1 + 30(3 + x4) = 29f3 [taking moments about f2]
30x4 = 29f3 - 20f1 - 90

49f1 + 29f2 = 30(26 - x4) [taking moments about f3]
30x4 = 780 - 49f1 - 20f2

but I can't isolate f1, f2 or f3. What mathematical technique do I need?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
To solve for the three unknown forces f1, f2, and f3, you will need to use a system of three equations with three unknowns. You can use substitution or elimination to solve the system of equations.
 

1. What is 'reversing' a moments calculation?

'Reversing' a moments calculation refers to the process of determining the original data or variables used to calculate a specific moment, such as the mean or standard deviation. It involves using the calculated moment and other known information to solve for the missing data.

2. Why would someone need to reverse a moments calculation?

There are various reasons why someone may need to reverse a moments calculation. One common reason is to verify the accuracy of the original data or to detect any errors in the calculations. It can also be useful for predicting future outcomes based on past data or for understanding the relationship between variables.

3. What are the steps involved in reversing a moments calculation?

The first step is to identify the moment that needs to be reversed, such as the mean or standard deviation. Then, gather all the known information, including the calculated moment, sample size, and any other relevant data. Next, use a formula or mathematical equation to solve for the missing data. Lastly, check the accuracy of the reversed moment by comparing it to the original data.

4. Are there any limitations to reversing a moments calculation?

Yes, there are some limitations to reversing a moments calculation. It is only possible if the original data or variables used in the calculation are known. If the data is incomplete or unavailable, it may not be possible to accurately reverse the moment. Additionally, the process may be more complex for moments that involve multiple variables or complicated equations.

5. How can reversing a moments calculation be helpful in scientific research?

Reversing a moments calculation can be helpful in scientific research in various ways. It can help validate the accuracy of data and identify any errors in the calculations. It can also aid in understanding the relationships between variables and making predictions based on past data. Additionally, it can provide insights into the underlying patterns and trends in the data, which can be useful in developing new theories or hypotheses.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
849
  • Introductory Physics Homework Help
Replies
3
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
27
Views
3K
  • Introductory Physics Homework Help
Replies
22
Views
2K
Back
Top