IB Physics IA: Spring Constant and Spring Length Flashcards

Flashcards covering the vocabulary, theoretical equations, variables, and evaluative conclusions from a Physics IA investigation on spring constants.

Hooke’s law

The relationship describing the restoring force, $F$, as proportional to the extension, $x$, defined by the equation $F = kx$.

Spring Constant ($k$)

A material property measured in $Nm^{-1}$ that determines the stiffness of a helical spring; a larger value indicates a stiffer spring.

Extension ($x$)

The distance in meters ($m$) by which a spring stretches when a load is applied.

Torsional Deformation

The twisting of the wire that occurs when a load is attached to a helical spring, which is the primary mechanism through which these springs operate.

Shear Modulus ($G$)

A property that measures a material's resistance to twisting; it remains constant for springs made of the same material regardless of their geometry.

Spring Rate Equation (Theoretical Model)

The formula $k = \frac{Gd^4}{8(D-d)^3N}$, where $d$ is wire diameter, $D$ is spring diameter, and $N$ is the number of active windings.

Active Windings ($N$)

The number of turns of wire on a spring, which is directly proportional to the spring length and inversely proportional to the spring constant (k \text{ } \boldsymbol{\text{\propto}} \text{ } \frac{1}{N}).

Independent Variable

The length of the spring, $L$, varied at lengths of $5$, $7$, $11$, $16$, and $22 \text{ centimeters}$.

Dependent Variable

The spring constant, $k$, calculated from the inverse of the gradient of the load-extension graph ($m = \frac{1}{k}$).

Control Variables

Factors kept constant including wire diameter ((1.00 \times 10^{-3} \text{\,m}) \boldsymbol{\text{\pm}} 0.02), spring diameter ((20.0 \times 10^{-3} \text{\,m}) \boldsymbol{\text{\pm}} 0.02), ambient temperature, and material (steel).

Gravitational Acceleration ($g$)

The value used to calculate applied load ($F = mg$), taken as $9.81 \text{\,ms}^{-2}$ or $9.81 \text{\,Nkg}^{-1}$.

Parallax Error

A type of observational error avoided in this experiment by ensuring the clamp and springs were arranged at eye-level view.

Uncertainty of Load (\boldsymbol{\text{\Delta}} F)

The absolute uncertainty calculated for the applied forces, determined to be approximately \boldsymbol{\text{\pm}} 0.0010 \text{\,N}.

$R^2$ Value

A statistical correlation coefficient; values between $0.9995$ and $0.9999$ in this experiment confirmed high linearity and the validity of Hooke’s law.

Inverse Proportional Relationship (Conclusion)

The research finding that k \text{ } \boldsymbol{\text{\propto}} \text{ } \frac{1}{L}, supported by the direct proportionality observed between the spring constant and the inverse of the length ($L^{-1}$).

Damping Mechanism

A suggested improvement to reduce oscillations and random error, such as using an air resistance plate or a small card in water.

Systemic Error (Identified Limitation)

The overestimation of the spring constant caused by the contributing mass of the spring itself, particularly affecting the $16.0$ and $22.0 \text{\,cm}$ springs.