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 the values with the sliders, or type a value in the box next to a slider and press Enter. A value outside the allowed range is set to the nearest allowed value.
▲ 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 on the slider 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.