Toys make excellent physics laboratories. A bouncing ball demonstrates
the coefficient of restitution — the ratio of energy preserved after
each collision. A paper airplane illustrates lift and drag — the same
forces that keep a Boeing 747 in the air. A yo-yo is a textbook
problem in rotational mechanics that children master intuitively long
before they encounter the equations.
What makes these simulations valuable is that you already have an
intuition for the objects. You know roughly how high a basketball
should bounce. You know a paper airplane throws better at a gentle
angle than straight up. These simulations let you verify and deepen
that intuition by adjusting the parameters and watching the physics
respond in real time.
There are no formulas to memorise here. Just throw, bounce, and
observe.
Coefficient of Restitution
COR = vrebound / vimpact. Determines how much
kinetic energy a ball keeps after bouncing. COR=1 is perfectly
elastic; COR=0 is a dead impact (no rebound).
Lift Force
L = ½ × ρ × CL × A × v². Air deflected downward by a wing
pushes the wing upward. Lift depends on speed squared — double the
speed, four times the lift.
Drag Force
D = ½ × ρ × CD × A × v². Air resistance opposing forward
motion. Also grows with v² — fast objects fight much more drag than
slow ones.
Energy Loss per Bounce
After n bounces: hn = h0 × COR2n.
Energy remaining = COR2n × 100%. A superball with
COR=0.92 still has 44% energy after 10 bounces; a steel ball
(COR=0.55) has only 0.5%.
Why does a superball bounce so much higher than a steel ball?
The coefficient of restitution (COR) measures how much kinetic
energy is preserved after impact. A superball (COR ≈ 0.92) retains
about 85% of energy per bounce. Steel (COR ≈ 0.55) retains only 30%,
because the hard surfaces convert most energy to heat and
sound.
Why does a paper airplane glide instead of falling straight
down?
As the plane moves forward, even a flat wing at a small angle
forces air downward. Newton's third law: air pushes the wing upward
— this is lift. Lift balances gravity and lets the plane glide. When
speed drops too low, lift vanishes and the plane descends.
What angle gives the best distance for a paper airplane?
Unlike a simple projectile (where 45° is optimal), a paper plane
flies best with a shallow 10–20° launch angle. This keeps the wing
at an efficient angle of attack throughout the flight, maximising
the lift-to-drag ratio and total glide distance.