←
Boss lesson · The Loading Ramp
Exam-hall rules, one ramp
score 0

Exam-hall rules, one ramp

This is the boss. No calculator: today g=10 m/s2g = 10\ \mathrm{m/s^2}, the round number every physicist keeps for mental work, and the ramp is pinned at 37∘37^\circ so that sin⁡37∘=0.6\sin 37^\circ = 0.6 and cos⁡37∘=0.8\cos 37^\circ = 0.8 — the 3-4-5 triangle, doing what it has done since Grade 9. Every value is chosen to fit in your head.

One crate, one long problem, and every answer feeds the next: the weight, then the press into the ramp, then the pull down it, then friction's cut of the press, then Newton on what survives, then the speed it all buys. Write each line down as you go — one early slip rolls the whole way to the bottom, and the finish screen will show you exactly where it started.

Then one bonus mark that uses no numbers at all, only the comparison this chapter has been building toward. 5★ under par here is the chapter crown. Clock in.

mW

W=mgW = m g

  • WW= Weight (force)
  • mm= Mass (mass)
Weight (W = mg) solver →
mmgNθ

N=mgcos⁡θN = m g \cos\theta

  • NN= Normal force (force)
  • mm= Mass (mass)
  • θ\theta= Incline angle (angle)
Normal Force on an Incline (N = mg cos θ) solver →
mmgF∥θ

F∥=mgsin⁡θF_{\parallel} = m g \sin\theta

  • F∥F_{\parallel}= Down-slope force (force)
  • mm= Mass (mass)
  • θ\theta= Incline angle (angle)
Weight Component Along an Incline (mg sin θ) solver →
Nfkμk

fk=μkNf_k = \mu_k N

  • fkf_k= Kinetic friction force (force)
  • μk\mu_k= Coefficient of kinetic friction
  • NN= Normal force (force)
Kinetic Friction Force (f = μₖN) solver →
aμkθ

a=g(sin⁡θ−μkcos⁡θ)a = g\left(\sin\theta - \mu_k \cos\theta\right)

  • aa= Acceleration (acceleration)
  • θ\theta= Incline angle (angle)
  • μk\mu_k= Coefficient of kinetic friction
Acceleration Down an Incline with Friction solver →
v0vat

v=v0+atv = v_0 + a t

  • vv= Final velocity (speed)
  • v0v_0= Initial velocity (speed)
  • aa= Acceleration (acceleration)
  • tt= Time (time)
Final Velocity (Uniform Acceleration) solver →
no calculator in the boss room — the numbers are chosen to fit in your head