Tools · Free play

Collision Lab

Pick a scene, change its numbers, and watch the momentum move: from one cart to another in a collision, out of a pair that a spring pushes apart, into a crate through the impulse of a push. The momentum bars and the chart show which totals stay fixed, and the readouts show the energy that impacts take away.

Choose a scene

Scene

Explore

Figure C.1 The chosen scene. Press Play or drag the time slider, and change the numbers in the panel (the motion is recomputed at once). Velocity arrows are green; at each impact, red arrows show the equal and opposite impact forces for a moment. In the momentum bars and chart, positive is to the right, and the black bar and green line are the total. On a crate, forces are drawn as in a free-body diagram: the weight ends at the center of gravity, a push ends on the face it acts on, and friction starts on the face it acts on.

Things to try

  1. Exchange of velocities. Equal masses, \(e = 1\), \(B\) at rest: \(A\) stops dead and \(B\) leaves at \(A\)'s speed.
  2. Stuck together. Set \(e = 0\). The carts move on together; the momentum total is unchanged and the energy lost is the largest possible.
  3. Newton's cradle on wheels. Three equal carts, \(e = 1\): the impulse passes down the line and only the last one leaves.
  4. A wall is not part of the system. A cart bouncing between walls reverses its momentum at every bounce: the walls' impulses are external. With \(e < 1\) each return trip is slower.
  5. Equal and opposite. Push two carts apart with a spring: their momenta are equal and opposite at every instant, and the total stays zero. Make one four times heavier.
  6. Start the clock when it moves. With a ramp push on a rough floor, the friction curve mirrors the push until the crate slips.
  7. Which \(e\) compresses the spring most? Try \(e = 0\), \(0.5\) and \(1\).
  8. A flatter bounce. Off a smooth floor, \(\tan\theta_2 = e\tan\theta_1\): the horizontal speed never changes.
  9. The billiards right angle. Equal pucks, \(e = 1\), any offset: the paths afterward are at \(90^\circ\).

How the lab works

The scenes on a straight track integrate Newton's second law for each body in small time steps (fourth-order Runge–Kutta, \(\Delta t = 0.5\ \text{ms}\)), with applied forces, springs and friction (static until the push exceeds \(\mu_s N\), then kinetic). Impacts are treated as instantaneous, as in the lessons: when two bodies meet, their velocities jump according to conservation of momentum and the coefficient of restitution, and the energy lost is recorded. Bodies that are pressed together stay in contact without bouncing.

The impulse of every force is added up step by step, so for each body \(m v - m v_0\) equals the sum of the impulses, to rounding: the principle of impulse and momentum, checked numerically. The bouncing ball and the pucks are computed exactly, from the projectile and straight-line motions between impacts.