Hooke's Law Flashcards

All 8 cards in this deck

State Hooke's law in words.

The extension of a spring is directly proportional to the force applied, provided the limit of proportionality is not exceeded.

What is the equation linking force, spring constant and extension, with units?

$F = k \times x$
force (N) = spring constant (N/m) $\times$ extension (m)

What does the spring constant tell you about a spring?

How stiff it is — the force needed per metre of extension (N/m). A larger $k$ means a stiffer spring.

What are the steps to calculate a spring constant from force and extension?
e.g. a force of $6$ N gives an extension of $4$ cm

1. Convert extension to metres: $4$ cm $= 0.04$ m
2. Rearrange $F = k \times x$ to $k = F \div x$
3. $k = 6 \div 0.04 = 150$ N/m

How do you find the spring constant from a force–extension graph?
e.g. the line passes through $(0.02$ m$, 5$ N$)$

Find the gradient of the straight-line part: $k =$ force $\div$ extension.
$k = 5 \div 0.02 = 250$ N/m

What is the difference between a linear and a non-linear force–extension relationship?

Linear: the graph is a straight line through the origin (extension proportional to force). Non-linear: the graph is curved, so extension is not proportional to force.

True or false? Extension is the same as the stretched length of the spring.

False. Extension = stretched length $-$ original (unstretched) length.

What is the name of the point on a force–extension graph beyond which the line stops being straight?

The limit of proportionality (beyond it, Hooke's law no longer applies).