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What is the difference between displacement and length in spring problems?
Displacement (Δx) is the change in length from the equilibrium position, while length is the total length of the spring.
Compare a spring with a high spring constant to one with a low spring constant.
High k: Stiffer, requires more force for the same displacement. | Low k: Less stiff, requires less force for the same displacement.
Compare stretching a spring vs. compressing a spring.
Stretching: Positive Δx, spring pulls back. | Compressing: Negative Δx, spring pushes back.
Compare the spring force at maximum displacement vs. at equilibrium.
Maximum displacement: Spring force is maximum. | Equilibrium: Spring force is zero.
Compare the energy stored in a stretched spring vs. a compressed spring (same |Δx|).
Stretched: Stores potential energy. | Compressed: Stores potential energy. Both store the same amount of potential energy if |Δx| is the same.
What happens when a spring is stretched (positive Δx)?
The spring exerts a force pulling it back towards its equilibrium position (negative force).
What happens when a spring is compressed (negative Δx)?
The spring exerts a force pushing it back towards its equilibrium position (positive force).
What is the effect of increasing the spring constant (k)?
The spring becomes stiffer, requiring more force to stretch or compress it by the same amount.
What is the effect of stretching a spring beyond its elastic limit?
The spring will deform permanently and not return to its original length.
What is the effect of the negative sign in Hooke's Law?
The spring force always opposes the direction of displacement, acting as a restoring force.
What is the difference between ideal and non-ideal springs?
Ideal springs have negligible mass and perfectly obey Hooke's Law. Non-ideal springs have mass and may not perfectly obey Hooke's Law.
Compare springs in series and springs in parallel regarding their stiffness.
Springs in series are more compliant (less stiff). Springs in parallel are stiffer.
How does displacement relate to force in springs arranged in series versus parallel?
In series, total displacement is the sum of individual displacements. In parallel, the total force is the sum of individual forces.