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

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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