Experiment 3: The Friction Ramp

Friction is the force you cannot switch off. It stops your slider, warms your hands and decides whether a block on a ramp stays put or slides. In this experiment you attack friction two ways: hands-on, by racing a slider over different surfaces, and in the simulation, where a block on a ramp reveals the clean mathematical rule a = g(sin θ − μ cos θ) — including the surprising angle below which the block refuses to move at all.

The physics behind the practical

On a ramp tilted at angle θ, gravity splits into two components: mg sin θ pulling the block down the slope and mg cos θ pressing it into the surface. Friction opposes sliding with a maximum strength of μ × the pressing force, where μ (mu) is the coefficient of friction — small for ice and waxed wood (about 0.05–0.2), large for rubber on rough surfaces (0.6 or more). While the block is stuck, static friction simply matches the downhill pull. Sliding starts only when the pull wins: mg sin θ > μ mg cos θ, which simplifies to tan θ > μ. The mass cancels — a heavier block presses harder but is also pulled harder, so the slip angle depends only on μ.

Once sliding, the net force is mg sin θ − μ mg cos θ, so the acceleration is a = g(sin θ − μ cos θ). That one line predicts everything the sim shows: zero acceleration in the "stuck zone", then a curve climbing toward g sin θ as friction's share shrinks. In the hands-on version, the same physics appears as distance: released from the ramp top, a low-friction slider keeps more of its energy as kinetic energy and runs further across the floor, while friction converts the rest to heat — rub the towel after several runs and you can feel where the energy went.

Variables and controls

In the virtual lab

Set ramp angle 20° and surface friction μ 0.20, press Release block, and read Acceleration, Slide time and Speed at bottom: expect about 1.51 m/s². Now raise μ to 0.60 at the same angle — the block will not move, because tan 20° = 0.364 < 0.60. Lower the angle step by step at a moderate μ and find where motion just stops: that critical angle satisfies μ = tan θ, which is a genuine laboratory method for measuring an unknown μ. Finally sweep the angle from 5° to 45° and watch the orange dot climb the acceleration-vs-angle curve in the Data Visualization panel, flat in the stuck zone, then rising. Log (angle, μ, acceleration) triples in the Observation Log.

Hands-on: surfaces on the ramp

Prop the board at a gentle, fixed angle, tape a start line near the top, and release the slider from rest on bare board, towel and wax paper in turn, three trials each, measuring how far it travels past the bottom. Keep the ramp angle, release point and slider identical — if the book stack slips mid-session, every later result is corrupted.

A worked investigation

The sim lets us test the formula precisely. Fix μ = 0.30 and vary the angle:

Step 1 — One full calculation. At 20°: a = 9.8 × (0.342 − 0.30 × 0.940) = 9.8 × (0.342 − 0.282) = 9.8 × 0.060 = 0.59 m/s². Note how close the race is: friction cancels 82% of the downhill pull, so a modest angle gives a gentle slide.

Step 2 — A complete run. At 20° with μ = 0.20 (a = 1.51 m/s²) down a 1.2 m ramp from rest: t = √(2s/a) = √(2.4 ÷ 1.51) = 1.26 s, and the speed at the bottom is v = at = 1.51 × 1.26 = 1.90 m/s — the sim's readouts agree.

Step 3 — The stuck test. At 20° with μ = 0.60: tan 20° = 0.364 < 0.60, so the formula would give a negative acceleration — the sim correctly shows no motion at all. Negative acceleration here is nature's way of saying static friction wins.

Step 4 — Measuring μ from an angle. For a mystery surface, raise the ramp until slipping just starts at 21.8°: μ = tan 21.8° = 0.40. One protractor reading has measured a material property.

Conclusion and evaluation

The acceleration data follow a = g(sin θ − μ cos θ) at every angle, and the stuck-zone boundary sits exactly where tan θ = μ. In the hands-on test the ranking by distance (wax paper furthest, towel shortest) matches the ranking by μ — two methods, one physics. Evaluation: the hands-on distance is a crude proxy, because the slider also loses energy hitting the floor join and sliding on the floor's own friction; repeat scatter of ±10% is typical. The sim removes those problems but assumes μ is identical everywhere on the surface, which real towel — bunched, worn, taped — is not. Trust the sim for the law, and the bench for the messiness of real materials.

Safety

Build the ramp on a stable stack that cannot topple, keep fingers out of the slider's path, and pick up sliders promptly — a block on the floor is a trip hazard in a busy room.

Common mistakes

• Pushing the slider "to help it start" — you have added an unknown force and destroyed the measurement.
• Letting the ramp angle drift between surfaces because the book stack settles — re-check the angle (or the books) before every set.
• Measuring distance from different start lines, or to the slider's front on one trial and its back on the next.
• Bunched towel or wrinkled wax paper — folds are extra obstacles, not extra friction.
• Confusing "more friction" with "heavier" — the slip angle does not depend on mass at all; μ and θ decide.

Exam Experience

Question 1 — calculation [4 marks]. A block rests on a ramp at 25° where the coefficient of friction is μ = 0.30. (a) Show that the block slides. (b) Calculate its acceleration.

Scoring guide:

• Compare tan 25° = 0.466 with μ = 0.30 [1]
• 0.466 > 0.30, so the downhill component exceeds maximum friction and the block slides [1]
• a = g(sin 25° − 0.30 cos 25°) = 9.8 × (0.423 − 0.272) [1]
• a = 1.48 m/s² down the ramp [1]

Question 2 — evaluation and design [4 marks]. Design an investigation to measure the coefficient of friction between a trainer sole and a wooden board, using only the board, books and a protractor. Explain how you would obtain a reliable value of μ.

Scoring guide:

• Place the trainer on the board and raise one end slowly until the trainer just begins to slide [1]
• At that critical angle, μ = tan θ [1]
• Repeat the measurement several times (re-seating the trainer each time) and average the angle before taking the tangent [1]
• Controls: same trainer, same contact area/orientation, board clean and dry, angle raised slowly to avoid overshoot [1]

Multiple choice 1. A block on a 15° ramp with μ = 0.40 does not slide because:

• A. Gravity does not act on ramps
• B. tan 15° = 0.27 < μ, so static friction can match the downhill pull
• C. The block is too heavy to move
• D. Friction always equals mg on a ramp

Answer: B. Sliding requires tan θ > μ; here 0.27 < 0.40, so friction balances the component of weight and net force is zero.

Multiple choice 2. On the high-friction towel, the slider stops much sooner than on wax paper. The kinetic energy it loses mainly becomes:

• A. Gravitational potential energy
• B. Heat in the surfaces
• C. Sound only
• D. Chemical energy

Answer: B. Friction converts ordered kinetic energy into thermal energy — the towel feels warm after repeated runs.

Going deeper: reading μ straight off the slip angle

There is a second, cleaner way to measure friction with nothing but this ramp: tilt slowly until the block *just* begins to slide, and note that critical angle θc. At the point of slipping, the along-slope pull exactly balances maximum static friction: mg sin θc = μs × mg cos θc, so the masses and g cancel and μs = tan θc. One group found their block slipped at 24°, giving μs = tan 24° = 0.445 — no stopwatch, no acceleration, just an angle and a tangent. Compare that with the kinetic μ from the sliding data (which used μ ≈ 0.30 in this lesson's table): static friction is usually the larger of the two, which is why objects resist starting to slide more than they resist continuing.

The distinction matters in the formula you already used: a = g(sin θ − μ cos θ) takes the kinetic μ once the block is moving, while the stuck-or-sliding test (tan θ vs μ) is governed near the boundary by the static value. Engineers exploit the gap deliberately — anti-lock brakes pulse to keep tyres at the edge of static grip rather than locked in weaker kinetic sliding. In your log book, always record which μ a number claims to be; a friction coefficient without that label is only half measured.