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

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SUMMARY

The correct calculation for the spring constant (k) using a spring scale stretched 10 cm under a force of 15 N is k = 1.5 N/cm. To determine the distance between adjacent 1.0 N marks on the scale, the formula F = kx is applied, resulting in a separation of approximately 0.67 cm. The misconception that the distance should be 1.5 cm arises from a misunderstanding of the relationship between force and displacement in springs. Proper unit management is crucial in these calculations to avoid errors.

PREREQUISITES
  • Understanding of Hooke's Law (F = kx)
  • Basic knowledge of force and units (Newtons and centimeters)
  • Ability to manipulate algebraic equations
  • Familiarity with spring scales and their applications
NEXT STEPS
  • Study the principles of Hooke's Law in detail
  • Learn about unit conversions and their importance in physics calculations
  • Explore the applications of spring constants in real-world scenarios
  • Practice solving problems involving force and displacement in springs
USEFUL FOR

Physics students, educators teaching mechanics, and anyone interested in understanding the behavior of springs and forces in practical applications.

RedBurns
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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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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.
 
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! 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
 
your right. I had everything flipped in my head
 

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