1.
Play with
this simulation for at least a few minutes.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.
Exercises Exploring Spring Forces
2.
With the simulation from the previous question, investigate how the spring force appears to be related to the displacement of the spring.
Definition 4.8.1. 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.
Exercises Practice with Spring Forces
1.
Explain how the expression in Hooke’s Law is consistent with your observations from the simulation (cite a specific observation!).
2.
Determine the units of the spring constant \(k\text{.}\) Why do you think these are appropriate units for this quantity?
Answer.
N/m
3.
What is the meaning of the negative sign in Hooke’s Law?
4.
Suppose you have a spring with a spring constant of \(k = 40 \mathrm{~N/m}\text{.}\) How far must you compress this spring for the spring force to reach \(5 \mathrm{~N}\text{?}\)
Answer.
\(0.125 \mathrm{~m}\)
