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Section 4.8 Spring Forces
You have now built quantitative models for the gravitational force and the frictional force. Next you will build a model for the spring force.
Activity 4.8.1 . Exploring Spring Forces.
(a) (b) With the simulation, investigate how the spring force appears to be related to the displacement of the spring.
Video Lesson 4.8.1 . Spring Forces.
Definition 4.8.2 . Hooke’s Law.
An ideal spring obeys Hooke’s Law, with a force that is linearly proportional to the displacement from equilibrium:
\begin{equation*}
\vec{F}^{S} = -k(\vec{x} - \vec{x}_{eq})
\end{equation*}
Assumption: An ideal spring is massless and does not deform when displaced from equilibrium.
Subsubsection Practice with Spring Forces
Activity 4.8.2 . Sensemaking: Observations.
Explain how the expression in Hooke’s Law is consistent with your observations from the simulation (cite a specific observation!).
Activity 4.8.3 .
Determine the units of the spring constant
\(k\text{.}\) Why do you think these are appropriate units for this quantity?
Activity 4.8.4 . Sensemaking: Sign.
What is the meaning of the negative sign in Hooke’s Law?
Activity 4.8.5 . Practice.
Suppose you have a spring with a spring constant of
\(k = 40 \mathrm{~N/m}\text{.}\) What is the magnitude of the displacement of the spring if the magnitude of the spring force is
\(5 \mathrm{~N}\text{?}\)
