Students practice identifying whether events on spacetime diagrams are simultaneous, colocated, or neither for different observers. Then students decide which of two events occurs first in two different reference frames.
Students move their left arm in a circle to trace out the complex plane (Argand diagram). They then explore the rectangular and exponential representations of complex numbers by using their left arm to show given complex numbers on the complex plane. Finally they enact multiplication of complex numbers in exponential form and complex conjugation.
A valuable model for figuring out how we're going to save the Earth
Let's start by visualizing the energy flow associated with driving a gasoline-powered car. We will use a box and arrow diagram, where boxes represent where energy can accumulate, and arrows show energy flow.
The energy clearly starts in the form of gasoline in the tank. Where does it go?
Actually ask this of students.
Visualize the energy as an indestructable, incompressible liquid.
“Energy is conserved”
The heat can look like
Hot exhaust gas
The radiator (its job is to dissipate heat)
Friction heating in the drive train
The work contribute to
Rubber tires heated by deformation
Wind, which ultimately ends up as heating the atmosphere
The most important factors for a coarse-grain model of highway driving:
The 75:25 split between “heat” and “work”
The trail of wind behind a car
What might we have missed? Where else might energy have gone?
We ignored the kinetic energy of the car, and the energy dissipated as heat in the brakes. On the interstate this is appropriate, but for city driving the dominant “work” may be in accelerating the car to 30 mph, and with that energy then converted into heat by the brakes.
Students take the inner product of vectors that lie on the spacetime axis to show that they are orthogonal. To do the inner product, students much use the Minkowski metric.