Tools · Free play

Force Lab

Pick a scene, change its numbers, and watch Newton's second law at work. The bars in the panel add up the forces along the motion at every instant, and they always land on \(ma\): when the push beats friction, when static friction gives way, when a spring's push fades, and when the forces balance and nothing accelerates.

Choose a scene

Scene

Explore

Figure F.1 The chosen scene. Press Play or drag the time slider, and change the numbers in the panel (the motion is recomputed at once). Forces are drawn as in a free-body diagram: the weight \(\colW{W}\) ends at the center of gravity, a push (the normal force, a spring, an applied push) ends on the face it acts on, and friction \(\colF{F_f}\) and a pull start where they act. The bars add the forces along the motion and land on \(\colMA{ma}\); velocity is green.

Things to try

  1. Too weak to move it. Push a \(20\ \text{kg}\) crate with \(60\ \text{N}\) on a floor with \(\mu_k = 0.3\): static friction matches the push, and the bars cancel to \(ma = 0\).
  2. The angle of repose. On the incline, set \(\mu_s = 0.5\) and raise \(\theta\) a degree at a time: the block holds until \(\tan\theta > 0.5\), at \(26.6^\circ\).
  3. Up, stop, and back? Send the block up a \(30^\circ\) slope at \(5\ \text{m/s}\). Friction points down the slope on the way up, then up the slope if it slides back. With \(\mu_s > \tan 30^\circ\), it stays at the top.
  4. The best pulling angle. With \(\mu_k = 0.4\), find the angle that gives the largest acceleration. It is \(\tan^{-1}0.4 = 21.8^\circ\).
  5. Static friction gives way. With a push that grows, the friction line follows the push up to \(\mu_s N\), then drops to \(\mu_k N\): the acceleration jumps.
  6. A push that fades. In the spring launch, the acceleration is largest at release and zero where the spring reaches its free length; the speed is largest there.
  7. Tension is not the hanging weight. With two blocks and a pulley, compare \(T\) with \(m_B g\) as you change the masses.
  8. The mass cancels. Slide to rest from \(8\ \text{m/s}\) with \(\mu_k = 0.4\), then change the mass: the stopping distance, \(v_0^2/2\mu_k g = 8.15\ \text{m}\), does not change.

How the lab works

The scenes integrate Newton's second law in small time steps (fourth-order Runge–Kutta, \(\Delta t = 0.5\ \text{ms}\)). At each step the forces along the track are added up: the applied force, the component of the weight along the slope, a spring's push, and friction. Friction is static while the body is at rest and the other forces fit within \(\mu_s N\), and kinetic, \(\mu_k N\) against the motion, once it slides. The normal force comes from the equation across the track, so an angled pull or a slope changes it. The two blocks and the pulley are solved exactly, from the equations of Lesson 4.