Presets
Playback
Ball and chain
Mass, chain length, release angle, damping and gravity.
Wall
Where the wall stands, how strongly its bricks are bonded and how bouncy the contact is.
Layers
Model checks
The science
The pendulum
A ball of mass m on a chain of length L swings with theta'' = -(g/L) sin(theta) - c theta' (c is a small damping). The equation is integrated with RK4 at 1 ms steps. The period is not constant for large swings: T = 4 sqrt(L/g) K(sin(theta0/2)) with K the complete elliptic integral of the first kind (computed by the arithmetic-geometric mean), which reduces to 2 pi sqrt(L/g) only for small angles.
Energy and speed
Released from angle theta0 the ball has potential energy m g L (1 - cos theta0) above the lowest point, so its peak speed is v = sqrt(2 g L (1 - cos theta0)). The wall face sits at a horizontal distance d from the plumb line; the ball touches it at theta_c = asin((d - r)/L) with kinetic energy m g L (cos theta_c - cos theta0), shown in the last graph.
Impact with the wall
The wall is a grid of 6 x 16 bricks (60 kg each), stacked and bonded. When the ball touches a brick, a one-dimensional collision with restitution e gives the brick the speed vb = (1 + e) m v / (m + Mb). The brick is knocked loose only if its kinetic energy Mb vb^2 / 2 exceeds the bond energy per brick; the ball then loses the momentum Mb vb. Otherwise the ball rebounds. Bricks with nothing under them fall; freed bricks fly ballistically and bounce on the ground.
Simplifications
Rigid chain (no stretch or sway), bricks never collide with each other, contact is treated brick by brick along the horizontal direction, bond energy is a single number instead of real mortar fracture mechanics. It is an educational energy-and-momentum model of an inanimate structure, not an engineering demolition tool.
What to try
- Start at 20 deg: the ball bounces off the wall because the impact energy stays under the bond energy.
- Drag the ball back to raise the release angle and watch the impact energy marker climb the curve.
- Pick On the Moon: the swing is much slower (period scales as 1/sqrt(g)) and impact energy drops six-fold.
- Double the ball mass: energy doubles but speed at the bottom does not change.