Hi
I did a physics lab where we hung one spring with several different masses and found its K value, then hung another spring with several different masses and found its K value, then we joined both the springs together and hung several masses on it, and then found the K value for that double spring,
but how would i get an equation for the K value of the double spring...relating back to the individual springs...basically what is Ktotal based on K1 and K2
some help would be greatly appreciated!
thank you
The k of two springs connected end-to-end is given by
1/k = 1/k1 + 1/k2
That is because the combined deflection is F/k1 + F/k2 = F * (1/k1 + 1/k2)
Divide that by the sprint tension F for the spring constant.
How does that agree with your measurements?
it works perfectly, i understand! thank you so much!
To determine the equation for the K value of the double spring (Ktotal) based on the individual springs (K1 and K2), you need to understand how springs in series behave.
In a series connection, when two springs are connected end-to-end, the total force exerted by the combined springs is equal to the sum of the individual forces of each spring. Similarly, the total extension or compression of the double spring is equal to the sum of the individual extensions or compressions of the two separate springs.
From Hooke's Law, we know that the force exerted by a spring is directly proportional to its extension or compression. Mathematically, this can be expressed as:
F = -kx
Where:
- F is the force exerted by the spring,
- k is the spring constant (K value), and
- x is the extension or compression from the equilibrium position.
Using this equation, we can now analyze the double spring system.
1. When a mass is hung on just the first spring:
The force exerted by the spring (F1) is given by F1 = -K1x1, where x1 is the extension or compression caused by the first mass.
2. When the same mass is hung on just the second spring:
The force exerted by the second spring (F2) is given by F2 = -K2x2, where x2 is the extension or compression caused by the second mass.
3. When the mass is hung on both springs:
For the double spring system, the total force exerted (Ftotal) is given by the sum of the forces from both springs:
Ftotal = F1 + F2 = -K1x1 - K2x2
Now, to find the total extension or compression (x) caused by the mass when hung on both springs, we need to consider that the total extension or compression (x) is the sum of the individual extensions or compressions (x1 and x2):
x = x1 + x2
From Hooke's Law for each spring, we can express the total force and total extension as follows:
Ftotal = -Ktotalx
Combining the equations, we have:
-K1x1 - K2x2 = -Ktotal(x1 + x2)
To relate the individual spring constants (K1 and K2) to the total spring constant (Ktotal), we can rearrange the equation:
-Ktotal(x1 + x2) = -K1x1 - K2x2
-Ktotalx1 - Ktotalx2 = -K1x1 - K2x2
(K1 - Ktotal)x1 + (K2 - Ktotal)x2 = 0
From this equation, we can deduce that the individual spring constants (K1 and K2) and the total spring constant (Ktotal) are related as follows:
K1 - Ktotal = 0
K1 = Ktotal
and
K2 - Ktotal = 0
K2 = Ktotal
Thus, we can conclude that the total spring constant (Ktotal) of the double spring system is equal to the individual spring constants (K1 and K2).
Therefore:
Ktotal = K1 + K2
So, to find the K value for the double spring, you can simply add the individual K values of the two separate springs.