Investigate how acceleration depends on resultant force and on total moving mass using a low-friction trolley on a runway or ramp, with a suitable motion sensor or light gates.Original labelled apparatus schematic; not to scale. Follow the stated measurements and safety instructions.
A hanging mass and string over a pulley can provide the driving force. Secure the pulley and ramp, keep the string taut and arrange a safe stop before the trolley falls off the track.
A slight ramp slope can balance friction; check this carefully. A steeper slope adds a larger force from gravity along the track and changes the resultant force.
Record the total accelerating mass: the trolley, added masses and hanging mass in a connected system. Do not equate the trolley's mass alone with the whole system's mass.
Method, controls and measurements
For the required ramp investigation, repeat runs with different added trolley masses at a fixed angle. Measure the downslope force with a suitable force sensor/newton meter in the school setup, and use timing or motion data to calculate acceleration. Do not assume adding mass leaves gravity's downslope force unchanged.
For an ideal trolley rolling freely down a fixed slope, doubling its mass also doubles the gravitational force along the slope. Its acceleration is therefore approximately unchanged if friction is negligible. This is different from adding mass while keeping the resultant force constant.
Check the trolley rolls freely and the sensor is aligned. Use a fixed release position and release without pushing, with enough track for measurements before the end stop.
As a controlled-force extension using a pulley, transfer masses from the trolley to the hanger so total moving mass stays constant while the hanging driving force increases. Measure the total mass once and check it remains constant.Alternative ramp/runway arrangement with light gates and a hanging drive. Account for all moving mass and friction; hanging weight is the driving force.
For the pulley mass investigation, keep the driving force fixed and add known masses to the trolley. Keep track angle, pulley, string and release procedure unchanged.
Calculate hanging driving force using weight = mg, with g supplied or about 9.8 N/kg. Resultant force on the whole moving system is driving force minus friction, including any uncompensated slope effect.
With two light gates, measure speeds using interrupt-card length divided by its blocking time. Acceleration = (final velocity − initial velocity)/time between the velocity measurements; identify which time the logger reports.
A motion sensor can give a velocity–time graph directly. Use the gradient over a suitable straight section to find acceleration, rather than interpreting the height of the graph as acceleration.
If a supplied method measures distance from rest at approximately constant acceleration, a = 2s/t². Use only when initial velocity is zero and acceleration is approximately constant; light-gate analysis is usually more direct. A force sensor/newton meter must measure the intended direction, not the full vertical weight as though it were the downslope resultant force.
Take several force or mass settings and repeat runs at each. Exclude runs affected by an identifiable collision, string slip or push, with a stated reason, and repeat the setting.
Graphs and evaluation
At constant mass, acceleration should increase in proportion to resultant force: F = ma. An acceleration–force gradient is 1/m, with acceleration vertically and force horizontally.
At constant resultant force, acceleration decreases as total mass increases. Plot acceleration against 1/m to test the inverse relationship; acceleration against mass is a curve.
Friction, the pulley’s resistance to starting or changing its rotation (inertia), and a string that is not horizontal can all affect the force. The hanging weight is therefore not always the exact resultant force. Repeating alone does not remove these consistent effects.
Measure interrupt-card length accurately, secure it so it does not rotate and align gates. A longer blocking interval can reduce relative timing uncertainty, but it should still represent local speed adequately.
Electronic timing reduces human reaction-time error. Check the motion sensor’s zero reading and calibration. Look at the recorded graph or readings, rather than accepting an acceleration shown on the display without checking it.
Make a conclusion from the measured trend and repeat spread; distinguish a driving force from a measured or estimated resultant force. Do not claim exact proportionality from one run.
Exam skills: planning, precision and evaluation
State what you change (the independent variable), what you measure (the dependent variable) and what you keep the same (control variables). Explain how you keep each control variable constant, rather than just saying “make it fair”.
Accuracy means how close a result is to the true value. Precision means how close repeated measurements are to each other. Resolution is the smallest change an instrument can show. More digits on a display do not automatically mean a more accurate result.
Repeat measurements for each condition, calculate a mean and describe how spread out the results are. This helps assess and reduce the effect of random errors. Repeating cannot fix an error that pushes results consistently in one direction (a systematic error), such as uncompensated friction reducing the driving force.
Repeatability means getting similar results when the same person repeats the same method with the same equipment. Reproducibility means getting similar results when someone else, or different suitable equipment, repeats the experiment. Results can be consistent but still inaccurate.
Check that instruments read zero correctly and are calibrated where needed. Read scales at eye level: looking from an angle can give a wrong reading (parallax error). Choose suitable ranges, measurement intervals and scale divisions (resolution).
Write down the original readings straight away in a table, with units in the headings. Use decimal places that match the instrument’s resolution. Keep the original data and round only when needed. Do not discard a result just because it differs from your prediction.
An anomalous result does not fit the pattern of the other results. Repeat that measurement and check the method. Only leave it out of a mean if you have a clear reason; state which result you excluded and why.
For continuous variables, plot the independent variable on the horizontal axis and the dependent variable vertically. Use sensible scales, units and a best-fit line or curve; do not automatically join every point or force the graph through zero.
Find the gradient of a straight best-fit line using a large triangle: vertical change ÷ horizontal change. For a curve, draw a tangent to estimate the gradient at one point. Explain what the gradient shows in this experiment, include its units and use measured values to support your conclusion.
Uncertainty describes the possible range around a measurement. For one reading on a scale, half the smallest division is a useful classroom estimate unless the question says otherwise. If you subtract two readings, both have uncertainty. Percentage uncertainty = absolute uncertainty ÷ measured value × 100. Follow the method specified in the question.
Use results as evidence and then explain what they mean. A pattern linking variables (a correlation) does not prove that one causes the other. If the ranges of repeat results overlap, a claimed difference may be less convincing. Keep conclusions within the range tested and suggest an improvement that tackles a specific error.
Mr Kidman's Classroom