Springs in Series Verse Parallel Find Spring Constant
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3 سال پیش
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I was working on my
I was working on my lawnmower and got to thinking about springs in series verse parallel and how this affects the spring constant and force.
So lets first recall the formula for force from a spring. It is force equals the spring constant k times the displacement of the spring x. So basically the larger the spring constant or the more you displace ( contract or elongate the spring) the more force the spring will counteract with. Below I have plotted a graph of the force of the y axis and the displacement x on the x axis. We can see if we plot the formula for the force from a spring of k times x it is linear function.s
Now lets find the equivalent spring constant for these spring in series. I have place the spring constant in units of newtons per meter. This means that per meter of elongation or contraction from nominal the spring will apply a resitant force in newtons. So for the blue spring 31 newtons per meter of strectch.
So the formula for the k or spring constant equivalent is 1 over k equivalent equals 1 over k1 plus one over k2 plus one over k3.
We can rearrange this to get what we are solving for k equivalent to one side and plug in our values. We get an equivalent spring constant of 8.1 newtons per meter. This value should always be less then the lowest spring constant value in series
Now for parallel we will use the same spring constants. To find the equivalent spring constant we add the individual k values
Plugging in our number we get 87 newtons per meter
Now we can use these equivalent spring constant values in the k times x force equation to find the force from elogongating or compressing a spring. This is assuming that there is a fixture in place to make all springs elongate or compress at the same rate. Same x value.
Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.
So lets first recall the formula for force from a spring. It is force equals the spring constant k times the displacement of the spring x. So basically the larger the spring constant or the more you displace ( contract or elongate the spring) the more force the spring will counteract with. Below I have plotted a graph of the force of the y axis and the displacement x on the x axis. We can see if we plot the formula for the force from a spring of k times x it is linear function.s
Now lets find the equivalent spring constant for these spring in series. I have place the spring constant in units of newtons per meter. This means that per meter of elongation or contraction from nominal the spring will apply a resitant force in newtons. So for the blue spring 31 newtons per meter of strectch.
So the formula for the k or spring constant equivalent is 1 over k equivalent equals 1 over k1 plus one over k2 plus one over k3.
We can rearrange this to get what we are solving for k equivalent to one side and plug in our values. We get an equivalent spring constant of 8.1 newtons per meter. This value should always be less then the lowest spring constant value in series
Now for parallel we will use the same spring constants. To find the equivalent spring constant we add the individual k values
Plugging in our number we get 87 newtons per meter
Now we can use these equivalent spring constant values in the k times x force equation to find the force from elogongating or compressing a spring. This is assuming that there is a fixture in place to make all springs elongate or compress at the same rate. Same x value.
Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.
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