Top: the friction needed to hold the block (mg sin θ) and the most static friction can give
(μsmg cos θ). The block slips where they cross. Bottom: the velocity while it slides — the gradient is a.
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Surface
m / kg
how
θ / °
tan θ
slipped?
a / m s⁻²
a / cos θ
Show components of W
How to use this simulation
Choose the surfaces and the mass of the block.
Set each value with ▼ and ▲ (hold to go faster; the ↑ ↓ keys or the mouse wheel in the box also work, Shift = ×10), or type a value in the box. ↺ puts it back to its start value. Outside the classroom range the box turns amber ⚠: fine to explore, but the lab can't do this.
Move the pointer over any graph (or tap it): a dashed line shows the values where it cuts each curve, or the values of the nearest data point.
▲ Tilt raises the ramp from the angle shown until the block slips — like lifting the board by hand.
The slip angle θslip is shown.
▶ Release puts the block at the top of the ramp at the angle in the box and lets go. If the angle is
steep enough, the block slides down and the v–t graph gives its acceleration.
Press ● Record after a run. The Data & analysis tab plots a/cos θ against tan θ.
Work through the Tasks tab and write explanations on your worksheet.
The physics
Resolve the weight: mg sin θ down the slope, mg cos θ into the slope, so FN = mg cos θ.
At rest: Ff = mg sin θ, and it can be at most μsFN.
It slips when mg sin θ > μsmg cos θ, i.e. tan θ > μs, so μs = tan θslip (mass cancels!).
Sliding (Newton's 2nd law — Blocks 3–4): ma = mg sin θ − μdmg cos θ ⇒ a = g(sin θ − μd cos θ).
Model: μ values are typical classroom values; the "investigation" surface matches the Forces investigation
(slip at 28°, a = 7.8 m s⁻² at 60°). The ramp is 1.00 m long; the block slides 0.80 m.
Newton's laws
The badge above the scene says which law applies at this moment: 1st law — at rest or moving at a constant velocity, the resultant force is zero (ΣF = 0); 2nd law — accelerating, ΣF = ma. The table under the free-body diagram adds up the forces (ΣF) and compares them with m a (▾ folds it). Tick 3rd-law pairs to see every force with its partner: the same size and type, in the opposite direction, acting on the other body (the Earth, the floor, the string, the fluid…).