How Is Spring Displacement Calculated with Zero Acceleration?

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SUMMARY

The calculation of spring displacement with zero acceleration involves the spring constant (k) of 350 N/m and the mass (m) of the box, which is 1.8 kg. The correct algebraic expression for spring displacement (X) at the moment when acceleration is zero is derived from the energy conservation principle, where kinetic energy equals potential energy stored in the spring. The expression can be formulated as X = (V^2 * m) / (2 * k), where V is the velocity of the box just before contact, measured at 0.43 m/s. The previously attempted rearrangement of the equation was incorrect, leading to an erroneous displacement value of 0.0308 meters.

PREREQUISITES
  • Understanding of Hooke's Law and spring constant (k)
  • Basic principles of kinetic and potential energy
  • Familiarity with algebraic manipulation of equations
  • Knowledge of Newton's laws of motion
NEXT STEPS
  • Study the conservation of mechanical energy in spring systems
  • Learn about Hooke's Law applications in real-world scenarios
  • Explore the derivation of spring displacement formulas
  • Investigate the effects of mass and velocity on spring compression
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Students in physics, engineers working with mechanical systems, and anyone interested in understanding spring dynamics and energy conservation principles.

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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