Students consider projectile motion of an object that experiences drag force that in linear with the velocity. Students consider the horizontal motion and the vertical motion separately. Students solve Newton's 2nd law as a differential equation.
A ping pong ball is thrown from the roof of Weniger Hall with an initial velocity that makes an angle \(\theta\) up from horizontal. The ball experiences a drag force that is proportional to its velocity.
Use Newton's 2nd Law to solve for the position of the ping pong ball for any value of time.
Hints:
- Consider the horizontal and vertical components of the motion separately.
- While you're planning and working on your solution, be prepared to answer the following questions:
- What are you doing right now?
- How will the result help you?
- How are you checking that the result is sensible?
This problem is too long to do in one go. I like to
If you want to skips parts, skip position and just ask for velocity.
Separating the Vertical Component of Velocity: Many students have trouble separating the differential equation for the vertical components of the velocity. They want to keep separate the drag and gravity.
\begin{align*} \frac{dv_y}{dt} +\frac{b}{m}v_y = -g \end{align*}
group Small Group Activity
120 min.
group Small Group Activity
10 min.
assignment_ind Small White Board Question
5 min.
assignment Homework
assignment Homework
Show that a Fermi electron gas in the ground state exerts a pressure \begin{align} p = \frac{\left(3\pi^2\right)^{\frac23}}{5} \frac{\hbar^2}{m}\left(\frac{N}{V}\right)^{\frac53} \end{align} In a uniform decrease of the volume of a cube every orbital has its energy raised: The energy of each orbital is proportional to \(\frac1{L^2}\) or to \(\frac1{V^{\frac23}}\).
Find an expression for the entropy of a Fermi electron gas in the region \(kT\ll \varepsilon_F\). Notice that \(S\rightarrow 0\) as \(T\rightarrow 0\).
assignment Homework
assignment_ind Small White Board Question
10 min.
assignment Homework
For each case below, find the total charge.
group Small Group Activity
30 min.
Cartesian Basis $S_z$ basis completeness normalization orthogonality basis
Student explore the properties of an orthonormal basis using the Cartesian and \(S_z\) bases as examples.assignment Homework
Shown below is a contour plot of a scalar field, \(\mu(x,y)\). Assume that \(x\)
and \(y\) are measured in meters and that \(\mu\) is measured in kilograms.
Four points are indicated on the plot.