Spring constant and uncertainty in spring constant calculation

In summary, the spring constant (k) and its uncertainty (sigma_k) can be calculated using the period (T), number of oscillations (N), mass (m), time, slope, and uncertainty in slope, with the formula k=[4(pi)^2]/slope and [k+/- (sigma_k)] = [4(pi)^2]/[slope +/- (sigma_k)]. The uncertainty in k is based on the percentage uncertainty of the slope.
  • #1
vcooper28
1
0

Homework Statement



The spring constant (k) and uncertainty in the spring constant(sigma_k) have to be calculated with the values available for: period (T), number of oscillations (N), mass (m), time, slope and uncertainty in slope. The spring constant can be done with the first equation but I have no idea how to calculate the uncertainty in the spring constant.

Homework Equations


k=[4(pi)^2]/slope

[k+/- (sigma_k)] = [4(pi)^2]/[slope +/- (sigma_k)]


The Attempt at a Solution

 
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  • #2
vcooper28 said:

Homework Statement



The spring constant (k) and uncertainty in the spring constant(sigma_k) have to be calculated with the values available for: period (T), number of oscillations (N), mass (m), time, slope and uncertainty in slope. The spring constant can be done with the first equation but I have no idea how to calculate the uncertainty in the spring constant.

Homework Equations


k=[4(pi)^2]/slope

[k+/- (sigma_k)] = [4(pi)^2]/[slope +/- (sigma_k)]

The Attempt at a Solution


The only uncertainty you have in k - given your formula - is the uncertainty in the slope.
There is no uncertainty in the constants like π, so you use the percentage uncertainty of the slope as the percentage uncertainty of k.
 
  • #3


As a scientist, it is important to consider the uncertainty in any calculation or measurement. In this case, the uncertainty in the spring constant can be calculated by propagating the uncertainties in the other variables (T, N, m, slope, and uncertainty in slope) using the appropriate error propagation formulas. This will give a range of values for the spring constant, with an associated uncertainty, that takes into account the uncertainties in the other variables. Additionally, it is important to repeat the experiment multiple times and calculate the average spring constant and its uncertainty to ensure accuracy and reliability of the results. This will also allow for the identification of any outliers or systematic errors in the data. Overall, by considering the uncertainty in the spring constant calculation, we can have a more accurate and robust understanding of the system being studied.
 

1. What is spring constant?

Spring constant, also known as force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a unit distance.

2. How is spring constant calculated?

Spring constant is calculated by dividing the applied force by the change in length of the spring. This can be expressed as k = F/x, where k is the spring constant, F is the applied force, and x is the change in length.

3. What is the unit of spring constant?

The unit of spring constant depends on the unit of force and length used in the calculation. In the SI system, the unit of spring constant is Newtons per meter (N/m).

4. Why is there uncertainty in spring constant calculation?

There can be uncertainty in spring constant calculation due to various factors such as limitations of measurement equipment, variations in the material and design of the spring, and errors in the applied force and change in length measurements.

5. How can we reduce uncertainty in spring constant calculation?

To reduce uncertainty in spring constant calculation, it is important to use precise and accurate measurement equipment, carefully record and analyze data, and conduct multiple trials to account for variations in the spring. Additionally, using springs with consistent material and design can also help reduce uncertainty.

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