1. An
object is shot on an angle and explodes in mid air. Show that the center of mass of the pieces of
the object follows the same parabolic trajectory that the object as a whole was
on. Ignore air resistance.
2. Show
that in air two objects of the same shape and composition but of different
sizes will fall at different rates.
3. Show
how momentum is conserved for a two body system (minimum) collision in two
dimensions.
4. Investigate
terminal velocity in a fluid.
5. Analyze
a simple pendulum (tension, K, U, period, etc.) of varying mass / length, and
then simulate and analyze a compound pendulum.
6. Investigate
the collision of launch projectiles.
7. Analyze
projectile ranges of objects launched via a spring along an incline with and
without friction.
8. Planetary
motion: Kepler’s Laws, decaying orbits, orbital
boosts.
9. Analyze
a mass bobbing up and down on a spring (tension, K, U, period, etc.) of varying
mass / spring constant with and without a drag force, and then simulate and
analyze a mass that is both swinging like a pendulum and bobbing up and down
(without drag).
10. Show that a
when a long, tall object—like a tree or chimney—falls, if it breaks on the way
down, it tends to do so about 2/3 of the way up from its base.
11. Analyze the
motion of a stationary rocket in outer space being bumped by a small asteroid
moving along a line perpendicular to the rocket. The asteroid could hit the rocket’s center of
mass, or it could hit else where. Deal
with conservation of energy, linear momentum, and angular momentum.
12. A time
variable force F acts on mass 1 for time t, which then collides into and passes
right through mass 2 in a frictionless environment. Analyze how final speed of mass 1 is related
to F, t, and the final speed of mass 2.
13. Investigate
escape velocity and how it relates to launch speed, mass of the planet, and
radius of the planet.
14. Investigate
apparent weight fluctuations of a person living at various latitudes as
rotational speed of her planet changes.
15. Analyze a
roller coaster: normal force at various locations in a loop-the-loop; minimum
speed needed down low to ensure coaster makes it around the loop; etc.
16. Simulate gears
or pulleys connected with belts. Analyze
torques, tensions, angular speeds and accelerations. Vary the radii or gears / pulleys.
17. Mass 1
attached to string of length L is raised a height h and release. It collides with mass 2 at bottom of swing,
which becomes a projectile.
18. Show that
if a sphere collides elastically but off center with another stationary sphere of
the same mass, the two will move in perpendicular directions after the
collision, regardless of the initial speed of the first mass.
19. Simulate a bridge. There are various types; choose one. Analyze the tensions at various places in the
bridge while static equilibrium.
20. Simulate
and analyze the formation of a planetary system: many masses initially far
apart, each with small velocities; mutual gravitational attraction;
conservation of angular momentum and gravitational potential energy of the
system.
21. Simulate a
rocket burning fuel at a constant rate, and analyze it motion in a gravity-free
environment.
22. Investigate
springs of varying spring constants in parallel, in series, and in various
combo arrangements.
23. Show that the
stars in a binary star system and in 3-star systems (which are not uncommon)
revolve about a common center of mass.
Then analyze the motion of two isolated, initially stationary stars as
they fall toward their center of mass. Analyze the time required and show that energy
is conserved.
24. Simulate a
simple turbine or fan. Analyze how its
angular speed is affected when forces are applied to the blades. Look at forces that vary in strength and direction
from one run to the next, and change the lengths and masses of blades.