Calculating Spring Constant: Why 1.5 cm Isn't the Correct Measurement

In summary, the spring scale has a force constant of 1.5 N/cm and the adjacent marks should be 0.66667 cm apart to accurately measure forces. This is because the force is linearly proportional to the distance on the scale.
  • #1
RedBurns
24
2
A spring scale is stretched 10 cm when a force of 15 N is applied to it. How far apart should adjacent 1.0 N marks be on the scale?

Why would 1.5 cm not be correct?

Force= Spring Constant* Change in spring from rest
15n=k*10 cm
k=1.5
 
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  • #2
Wouldn't it be 0.66 cm? If there are 15 marks within 10 centimeters, there should be a mark every 2/3 of a centimeter. I may be reading this question wrong, though.
 
  • #3
RedBurns said:
A spring scale is stretched 10 cm when a force of 15 N is applied to it. How far apart should adjacent 1.0 N marks be on the scale?

Why would 1.5 cm not be correct?

Force= Spring Constant* Change in spring from rest
15n=k*10 cm
k=1.5

For starters, watch the units! You are dividing N by cm! :grumpy: NOT a good habit to get into. The good news is, since you are using this k to calculate a distance in cm you can get away with it.

Otherwise:
F = kx
15 N = k(10 cm)
k = 15 N/10 cm = 1.5 N/cm.

Now, set F = 1 N. (Since F is linear in x, this will be the separation between 1 N marks.)

F = kx
1 N = (15 N/cm)x
x =1 N/(15 N/cm) = 0.66667 cm.

My tip to all my students, anyways, is to ALWAYS write out your work, even if it seems easy enough to do in your head. (Perhaps especially when!)

-Dan
 
  • #4
your right. I had everything flipped in my head
 

1. What is the importance of accurately measuring the length of a spring when calculating its spring constant?

Accurately measuring the length of a spring is crucial in calculating its spring constant because it is one of the key variables needed in the formula for spring constant (k=F/x). A small error in the measurement can lead to a significant difference in the calculated value of the spring constant.

2. Why is 1.5 cm not the correct measurement for determining the spring constant?

1.5 cm is not the correct measurement for determining the spring constant because it does not provide enough precision. The smaller the measurement, the more accurate the calculation will be. Additionally, 1.5 cm may not accurately represent the original length of the spring due to factors such as stretching or compression.

3. Can using an incorrect measurement for spring constant affect the results of an experiment?

Yes, using an incorrect measurement for spring constant can greatly affect the results of an experiment. The spring constant is a crucial factor in determining the relationship between force and displacement in a spring, and an incorrect measurement can lead to inaccurate conclusions and results.

4. How can I ensure an accurate measurement of a spring's length?

To ensure an accurate measurement of a spring's length, it is recommended to use a ruler or caliper with smaller units of measurement (such as millimeters) and to take multiple measurements at different points on the spring. This will help minimize errors and provide a more precise measurement.

5. Are there any other factors that can affect the spring constant besides the length of the spring?

Yes, there are other factors that can affect the spring constant, such as the material and thickness of the spring, the temperature, and the amount of force applied. It is important to control these variables in an experiment to accurately calculate the spring constant.

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