Frequently Made Errors in Mechanics - Springs - Comments

[haruspex]

haruspex submitted a new PF Insights post

Frequently Made Errors in Mechanics - Springs

Continue reading the Original PF Insights Post.

 

[QuantumCurt]

That was a good write up. I've been tutoring a bit of freshman level physics this last year (during my sophomore year), and I've had to correct some similar errors that people were making. It was made more difficult because these students had not yet completed any E&M, so I was unable to use the analogy of adding resistors in series and parallel. I've found that identifying and helping people with these frequently made errors has really improved my own knowledge of the material.

 

[Greg Bernhardt]

haruspex is on a writing tear at the moment. When I get a chance I'm going to link all his entries together. It's a wonderful collection.

 

[Merlin3189]

Sec 1 -There seems to be a small typo in the 6^th line here

Attempted answer:
When the tension in the first spring is T, the tension in the second spring will also be T.
The two extensions will be $\frac{T}{k_1} and \frac{T}{k_2}$
Total extension $= T(\frac{1}{k_1}+\frac{1}{k_2})$
X Total tension = 2T
Overall spring constant $= \frac{2T}{T(\frac{T}{1}k_1+\frac{1}{k_2})}=\frac{2k_1k_2}{k_1+k_2}$

I think it should be
Overall spring constant $= \frac{2T}{T(\frac{1}{k_1}+\frac{1}{k_2})}=\frac{2k_1k_2}{k_1+k_2}$

Reference https://www.physicsforums.com/insights/frequently-made-errors-mechanics-springs/