Accelerating reference frames cause simple motion to appear complicated.

Estimated Time: 20 minutes, including wrap-up

Students are asked to draw the trajectory of a ball thrown straight up on the station platform as seen from a train accelerating through the station, for several values of the (constant) acceleration.

Basic familiarity with Newtonian mechanics for constant acceleration. Know the definition of trajectory (can be defined quickly). Optional but helpful: motion diagrams (object is represented as a dot for equal time intervals)

• Small whiteboards with markers
• Pictures (transparencies or electronic) of several sample trajectories to show as solutions to students

• Some students draw motion diagrams, other draw trajectory graphs, but the students who draw motion diagrams seem to have a better understanding that the coordinate system is changing position in a time dependent way.
• Some students don't recognize the parabolic shape is preserved (just rotated) - some students don't want to call this a parabola because it does not pass the vertical line test.

• First discuss the case of zero acceleration, but nonzero velocity, that the trajectory a parabola (the same as if the train is not moving but the ball has a non-zero horizontal component to the velocity).
• Then slowly increase the acceleration (opposite to the velocity) (the parabola rotates so that the symmetry line is no longer vertical).
• Is a boomerang trajectory possible? (Boomerang here means stops at the same location that it started - it actually looks like a line rather than a loop.)
• Show prepared pictures/graphs if appropriate.

See this page for further discussion.

Which way does gravity (appear to) point on the train?