Students observe the motion of a puck tethered to the center of the airtable. Then they plot the potential energy for the puck on their small whiteboards. A class discussion follows based on what students have written on their whiteboards.
Students observe the motion of a puck tethered to the center of the airtable. Then they plot the potential energy for the puck on their small whiteboards. A class discussion follows based on what students have written on their whiteboards.
Students begin this activity by observing the motion of the puck on the airtable. The puck is pushed so that it passes close to, but does not strike, the pin in the center of the table. Students are asked to observe the motion of the puck. Then students are asked to respond, “On your small white board, make a plot of the potential energy.” Don't give a more precise prompt.
After students have made their plots, the class discusses a variety of student responses.
This question is deliberately ambiguous to encourage a diversity of answers. This elicits responses that reveal information about what the students think is important about what they observed and what they expect to be thinking about with this type of problem.
Since the question is worded ambiguously, students draw a variety of plots including:
After discussing several student responses, it is useful to ask the students whether or not they think the force acting on the puck is a central force and to justify their answer. This typically leads to a review of the properties of a central force.
While confirming that many different representations are correct, and may be useful in certain circumstances, there is a conventional representation that is commonly used, with which they should be familiar.
It is important to mention that for central force problems, physicists typically write down the potential energy as a function of \(r\) since the force between the particles is only a function of the distance between them. Make sure that the students have the opportunity to see this graph and think about which parameters are shown.
assignment Homework
(Synthesis Problem: Brings together several different concepts from this unit.) Use effective potential diagrams for other than \(1/r^2\) forces.
Consider the frictionless motion of a hockey puck of mass \(m\) on a perfectly circular bowl-shaped ice rink with radius \(a\). The central region of the bowl (\(r < 0.8a\)) is perfectly flat and the sides of the ice bowl smoothly rise to a height \(h\) at \(r = a\).
assignment Homework
Consider a mass \(\mu\) in the potential shown in the graph below. You give the mass a push so that its initial angular momentum is \(\ell\ne 0\) for a given fixed value of \(\ell\).
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assignment Homework
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Students write python programs to compute and visualize the potential due to four point charges. For students with minimal programming ability and no python experience, this activity can be a good introduction to writing code in python usingnumpy
and matplotlib
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computer Mathematica Activity
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computer Mathematica Activity
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Students compute probabilities and averages given a probability density in one dimension. This activity serves as a soft introduction to the particle in a box, introducing all the concepts that are needed.assignment Homework
Find an expression for the free energy as a function of \(T\) of a system with two states, one at energy 0 and one at energy \(\varepsilon\).
From the free energy, find expressions for the internal energy \(U\) and entropy \(S\) of the system.
Plot the entropy versus \(T\). Explain its asymptotic behavior as the temperature becomes high.
Plot the \(S(T)\) versus \(U(T)\). Explain the maximum value of the energy \(U\).