How Is Spring Displacement Calculated with Zero Acceleration?

AI Thread Summary
The discussion focuses on calculating the spring displacement when the acceleration of a box is zero. The spring constant is given as 350 N/m, and the box has a mass of 1.8 kg with a speed of 0.43 m/s before contact. The user attempts to derive the displacement using the equations of motion and spring force but finds their calculation incorrect. They express uncertainty about rearranging the equations properly and seek clarification on the correct approach. The conversation highlights the need to consider all forces acting on the box, particularly under the assumption of vertical motion.
Paulbird20
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Suppose the spring has a spring constant of 350 N/m and the box has a mass of 1.8 kg. The speed of the box just before it makes contact with the spring in 0.43 m/s.

What is the algebraic expression for the magnitude of the spring's displacement at the instant when the acceleration of the box is zero? Express your answer in terms of the mass m of the block, the spring constant k, and the magnitude g of the acceleration due to gravity. (Answer using m to be the mass of the block, k to be the spring constant, and g to be the acceleration due to gravity).
Magnitude of spring's displacement = ?

Ok, from my notes i have spring F = K(constant for spring) * change in distance.

and also

V^2 = K* X^2 / M(mass)

and i re arranged that to V^2* M / K = X^2
i used this equation to get X = .0308 (meters?) and it shows as incorrect.

I think i may have re arranged the equation wrong but I am not sure any help would be great. TY
 
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Paulbird20 said:
Suppose the spring has a spring constant of 350 N/m and the box has a mass of 1.8 kg. The speed of the box just before it makes contact with the spring in 0.43 m/s.

What is the algebraic expression for the magnitude of the spring's displacement at the instant when the acceleration of the box is zero? Express your answer in terms of the mass m of the block, the spring constant k, and the magnitude g of the acceleration due to gravity. (Answer using m to be the mass of the block, k to be the spring constant, and g to be the acceleration due to gravity).
Magnitude of spring's displacement = ?

Ok, from my notes i have spring F = K(constant for spring) * change in distance.

and also

V^2 = K* X^2 / M(mass)

and i re arranged that to V^2* M / K = X^2
i used this equation to get X = .0308 (meters?) and it shows as incorrect.

I think i may have re arranged the equation wrong but I am not sure any help would be great. TY
No acceleration implies Newton 1. Identify all forces acting and apply it. I assume the box is falling vertically?
 

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