Inclined Plane Friction Lab (2D)

What happens

A block rests on a ramp. Gravity pulls it straight down; the ramp pushes back perpendicular to its surface (normal force) and, when the block tends to slide, along the surface (friction). Raise the ramp and the pull along the slope grows while the normal force shrinks, until friction can no longer hold the block.

Equations

Weight W = m g, component along the slope W sin(theta), normal force N = m g cos(theta). Static friction can supply up to mu_s N, so the block holds while |m g sin(theta) + F_ext| <= mu_s m g cos(theta). With no push this gives the critical angle theta_c = arctan(mu_s), independent of mass and gravity.

Once sliding, kinetic friction mu_k N opposes the motion: a = g (sin(theta) - mu_k cos(theta)) + F_ext / m. The work done by friction is mu_k N d and equals the mechanical energy lost: E_start - E_now = W_friction.

Honest simplifications

Coulomb friction is an empirical law with constant coefficients (the real ones depend on speed, surface condition and contact time). The block is a point-like rigid body that never tips or bounces; the end stop at the bottom stops it instantly. Both views share the same physics module.

Checks in the page

Check 1 starts a block just below and just above arctan(mu_s) for a reference surface and confirms it holds or slides. Check 2 compares the simulated distance after 0.8 s with 1/2 a t^2. Check 3 confirms that the energy lost equals the friction work.

• Raise the angle slowly until the block lets go: the critical angle is arctan(mu_s).
• Press Give a push on a ramp below the critical angle: kinetic friction slows it and static friction holds it again.
• Choose Ice on metal: the block slides at almost any angle.
• Pick Moon gravity: weight, normal force and friction shrink together, so the critical angle does not change.