Ticker Tape and Free-Fall Experiment: O-Level Physics Kinematics Practical

This is the critical fact that makes the whole experiment work. Because the interval is fixed by the mains frequency rather than by your reaction time or any mechanical setting, every measurement of distance between dots can be converted into a velocity with confidence. You are not relying on a stopwatch at all.

There are two common types of ticker timer used in O-Level labs:

• Electromagnetic (vibrating-strip) timer. A steel strip vibrates at the mains frequency and presses against a carbon paper disc to leave dots. It runs on AC from a low-voltage power supply (typically 4--6 V AC).
• Spark timer (or scaler timer). A high-voltage spark burns a hole through carbon paper. Spark timers can operate at both 50 Hz and alternative frequencies, so always confirm which frequency setting is in use. For O-Level work, 50 Hz is standard.

The key relationship to memorise is: each dot interval = 0.02 s, so counting dot gaps (not dots themselves) gives you the number of intervals. If you count 5 gaps between 6 consecutive dots, that represents 5 x 0.02 s = 0.10 s of elapsed time.

2 | Two experiments on one rig

The ticker timer sits at the core of two distinct O-Level kinematics experiments. Both use the same piece of equipment but address different physical situations.

(a) Trolley down a friction-compensated ramp

A dynamics trolley is placed on a slightly tilted runway. A piece of tape is attached to the trolley and threaded through the timer, which is fixed at the top of the ramp. When released, the trolley accelerates down the slope and pulls the tape through the timer.

The ramp must be friction-compensated: tilted at just the right angle so that, if you give the trolley a gentle push (with the timer switched off), it moves at constant velocity. At this angle, the component of gravity along the slope exactly cancels rolling friction. Any steeper tilt then gives a net force and a measurable uniform acceleration. This matters because it means the acceleration you extract from the tape is due entirely to the extra tilt (or an attached hanging mass), not a mixture of gravity and friction.

(b) Free-fall mass

A known mass (typically 1 kg) is attached to one end of a tape. The tape is threaded vertically through a timer clamped to a retort stand with the timer at the top. A soft landing (folded cloth or foam mat) is placed below. When the mass is released from rest, it falls under gravity and pulls the tape downward through the timer. In ideal conditions, the acceleration recorded on the tape should equal g, the acceleration due to gravity.

Both experiments produce a tape with dots spaced progressively further apart as the object accelerates. The analysis method -- the strip chart -- is identical for both.

3 | Apparatus

4 | Method

The procedure below covers both experiments. Steps 1 to 4 are common; step 5 branches depending on which variant you are running.

1. Set up the timer. Clamp the timer securely at the top of the ramp (ramp experiment) or to the retort stand (free-fall experiment). Thread the tape through the timing mechanism so it runs freely without catching on the sides.
2. Attach the tape. For the ramp experiment, attach one end of the tape to the trolley. For the free-fall experiment, attach one end to the 1 kg mass and allow it to hang so the tape runs vertically through the timer.
3. Switch on the timer first. This is an important procedural detail. Always start the AC supply and confirm the timer is running (you will hear it vibrating) before releasing the trolley or mass. If you release first, the first few centimetres of tape will have no dots, and you will lose data from the initial part of the motion.
4. Release and let the tape run. For the ramp experiment, release the trolley gently from the top of the ramp. For the free-fall experiment, hold the mass steady, then release it cleanly (do not push). Allow the full length of tape to pass through the timer before switching off.
5. Retrieve the tape. Switch off the power supply, then carefully remove the tape. Write a note on the tape (pencil on the back) to record which experiment it belongs to and the date.
6. Identify the usable section. Locate the first clear, evenly-printed dot. The very first few dots at the start of the tape are often unclear or overlap because the tape was not yet moving. Similarly, the last few dots of the free-fall tape may be irregular if the mass hit the landing before the tape cleared the timer.

5 | The chart-segment method

Raw dot spacing is very small and hard to read directly from the tape. The chart-segment (strip chart) method converts the tape into a visual velocity-time histogram.

Step 1: Choose your interval size. Cut the tape into strips of equal numbers of dot gaps. The most common choice for O-Level is 5 dot gaps per strip (sometimes called a 5-dot strip). Each strip therefore spans 5 x 0.02 s = 0.10 s.

A 10-dot strip (0.20 s) is also valid -- it gives fewer strips but each is longer and easier to measure. For slow accelerations (gentle ramp), a 5-dot strip may be too short to show a clear trend; switch to 10-dot strips in that case.

Step 2: Cut carefully. Mark the start of every fifth dot gap from your chosen start point. Cut along these marks. You should obtain 6 to 10 strips from a useful tape.

Step 3: Measure each strip. Use a ruler to measure the length of each strip in centimetres. Record these lengths in order (first strip, second strip, and so on).

Step 4: Paste side-by-side. On graph paper, draw a horizontal baseline. Paste each strip vertically in order, with its bottom touching the baseline, each strip adjacent to the previous one. Space them equally apart -- a few millimetres is enough.

Step 5: Read the chart. Because each strip spans the same time interval (0.10 s), the length of each strip is proportional to the average velocity during that interval. A strip that is twice as long represents twice the average velocity. The chart is therefore a velocity-time histogram. If the acceleration is constant, the strip lengths should increase by equal amounts, and the tops of the strips should lie along a straight line.

6 | Reading acceleration from the strip chart

The strip chart gives you a direct way to calculate acceleration. The length of each strip equals the distance travelled in one time interval (0.10 s), so the average velocity for each interval is:

$$v_{avg} = \frac{\text{strip length (cm)}}{0.10 \text{ s}}$$

The acceleration is the gradient of the best-fit line through the strip tops. You can calculate it directly from the strips without plotting:

$$a = \frac{v_{final} - v_{initial}}{t_{total}}$$

where $v_{final}$ is the average velocity represented by the last strip, $v_{initial}$ is the average velocity represented by the first strip, and $t_{total}$ is the time from the midpoint of the first strip to the midpoint of the last strip.

Worked example

Suppose you cut five 5-dot strips from a ramp tape and measure the following lengths:

Each strip spans 0.10 s, so the average velocity for each strip = strip length / 0.10.

The velocity increases from 20 cm/s to 60 cm/s. The time from the midpoint of strip 1 to the midpoint of strip 5 is 4 x 0.10 s = 0.40 s (four intervals between the midpoints of five consecutive strips).

$$a = \frac{60 - 20}{0.40} = \frac{40}{0.40} = 100 \text{ cm/s}^2 = 1.0 \text{ m/s}^2$$

The velocity increases by exactly 10 cm/s per strip in this example, which is the hallmark of uniform acceleration. In real data, the increases will be approximately equal but not perfectly so -- use the best-fit line gradient rather than comparing individual adjacent strips.

The "average velocity at a midpoint" interpretation

Each strip length represents the average velocity over that strip's 0.10 s interval. By the mean-value theorem, this equals the instantaneous velocity at the midpoint of the strip's time interval. This is the justification for treating each strip's average velocity as a single data point located at the strip's time midpoint when you plot a velocity-time graph.

7 | Free-fall specifics

When you run the free-fall version, two features of the tape deserve special attention.

Why the first few dots are too close together

When you switch on the timer before releasing the mass, the tape is momentarily stationary. The first three to five dot gaps are so close together they may be indistinguishable. Discard them and begin your strip analysis from the first dot gap that is clearly wider than its predecessor. Including these compressed dots in your first strip artificially shortens it, making the apparent initial velocity too low and inflating the calculated acceleration.

Why the last few dots show air-resistance flattening

As the mass falls faster, drag on the tape increases. At high speeds the dot spacing stops growing at the same rate, and the tops of the final few strips fall below the linear trend on the strip chart. Discard the last one or two strips if they deviate clearly below the best-fit line.

8 | Error analysis

9 | Why experimental g is typically less than 9.81 m/s²

Students running the free-fall tape experiment consistently report values of g between 9.1 and 9.4 m/s². The four systematic error contributions, ranked from largest to smallest, are:

1. Air resistance on the paper tape (largest contribution). The tape is light, wide, and flexible. As the mass falls, the tape is dragged upward through the surrounding air, exerting a drag force that opposes downward acceleration. This accounts for the majority of the 0.4 to 0.7 m/s² shortfall.
2. Friction in the timer slot. Even with careful threading, the tape rubs against the timer mechanism, adding a consistent upward retarding force on the falling mass.
3. Carbon paper and vibrating-strip resistance. The vibrating strip makes brief mechanical contact with the tape at each dot. At 50 Hz this averages out, but still adds a small, irregular resistance.
4. Mains frequency drift (smallest contribution). Mains frequency varies by approximately ±0.1 Hz, shifting the dot interval by ±0.002 s. This introduces at most a 0.2% error in the calculated acceleration -- well below the effect of friction and air resistance.

The short answer for an exam question: air resistance on the tape and friction in the timer both act upward on the tape, reducing the net downward force on the mass-plus-tape system below $mg$, so the measured acceleration falls short of the true value of g.

10 | Planning-style variant: how acceleration varies with ramp angle

The ticker tape experiment is a classic base for a planning question on O-Level Physics Paper 3. A common prompt is:

"Design an experiment using a ticker timer and trolley to investigate how acceleration varies with ramp angle."

A complete planning answer needs:

• Independent variable: angle $\theta$ of the ramp, varied across at least five values (for example 5°, 10°, 15°, 20°, 25°)
• Dependent variable: acceleration $a$ extracted from the strip chart at each angle
• Controlled variables: same trolley, same ramp surface, same timer and power supply; re-apply friction compensation at each angle

Procedure in brief: Friction-compensate the ramp at each new angle, switch on the timer, release the trolley, retrieve and analyse the tape. Take three repeats per angle and average.

Expected result: With friction compensated, $a = g\sin\theta$. A plot of $a$ against $\sin\theta$ gives a straight line through the origin; the gradient equals $g$.

Safety: fit a buffer block at the bottom of the ramp to prevent the trolley from flying off.

11 | Where this fits

The ticker tape method is one of several ways to measure acceleration and g at O-Level. Each method has different sources of systematic error, which is why comparing them is useful for building a complete picture.

For the classic string-and-pendulum approach to measuring g, see the Simple Pendulum Experiment O-Level Physics Measuring g. The pendulum is less affected by tape friction but introduces its own timing and air-resistance corrections.

For a modern digital approach, Measuring g Using Smartphone Pendulum shows how an accelerometer app can time oscillations with millisecond precision, reducing reaction-time error almost entirely.

Graph work -- reading the gradient from a strip chart, choosing appropriate scales, drawing a best-fit line through points with scatter -- is covered in depth in the O-Level Physics Graphing and Linearisation Clinic.

For a systematic treatment of all the error types that appear across O-Level Physics Paper 3 questions -- random, systematic, parallax, reaction time -- visit the O-Level Physics Error and Uncertainty Masterclass.

Sources

• SEAB 2026 O-Level Physics syllabus (6091): https://www.seab.gov.sg/docs/default-source/national-examinations/syllabus/2026/2026-o-level-syllabus/6091_y26_sy.pdf

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