Finding K in a two spring system.

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To determine the effective spring constant (k) for a two-spring system, the individual spring constants (K1 and K2) can be added together, resulting in the equation force = (K1 + K2)x. The participant confirmed their individual spring constants as K1 = 3.655 and K2 = 3.828, leading to an effective k of approximately 7.9000 when combined. They noted that the springs' performance varied due to wear, affecting the consistency of k values. The discussion clarified that when both springs are connected to a glider, the displacement x should be considered positive regardless of the direction of force applied. The thought process regarding the relationship between individual and combined spring constants was validated.
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Homework Statement


I did a lab experiment this past week and not sure how to determine k for a two spring system. We had an object on a frictionless surface and attached one spring on each side. I was able able to determine the spring constant for both springs individually but not sure how to determine the k for both springs acting together.

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The Attempt at a Solution



Was thinking force= kx so k for both springs could I do force= K1x-K2x. K1 is spring constant for spring on the left. X is positive since the spring is elongating. K2 is the spring attached on the left side of the glider. X is negative because the spring is compression. Am I on the right path?
 
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To be more clear. I have the value for k for each spring and both springs working together. I curious in finding how the two individual spring constants relate to the spring constant of the two spring system.
 
They should add. What values of k did you get for each situation?
 
Makes sense the K are added. Think I over thought it . I can imagine the two springs as one spring once they are connected to the glider. The x wouldn't be negative for K2 since it one spring. X would just be the distance the glider moves from equilibrium. force=(k1+k2)*x

for two springs system I got k= 7.9000
left spring k= 3.655
right spring k= 3.828

So if I add it together it is roughly close to where I should be. The springs were pretty crappy so it was tough to get a constant k with them the more you used them. Please let me know if this thought pattern is correct.
 
Yeah I mean if you pull the object one direction it is pushed by one spring in one direction and and pulled in that same direction by the other spring.
 
That makes sense. Thanks for the clarification
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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