C. Forces · ForcesPlanning and Conducting a Forces Inquiry
C2.5 C2.4 A1.12About 75 minutes
Learning goals- I can plan an inquiry about forces in one dimension: question, hypothesis, variables, procedure, safety and data table.
- I can use free-body diagrams, vector diagrams and Newton's laws to make predictions and analyse results.
- I can use SI units, convert from imperial units, and record measurements with sensible precision.
- I can analyse data with a graph, find a slope, and evaluate my results and sources of error.
Words to know
hypothesis
A testable statement of what you expect to happen and why, often written "If ..., then ..., because ...".
fair test
An investigation in which only the independent variable is changed; all other variables are controlled.
precision
How finely a measurement is made (e.g. to the nearest 0.1 N), shown by its number of significant digits.
random error
Unpredictable variation between repeated measurements. Reduced by repeating trials and averaging.
systematic error
An error that shifts every measurement the same way, such as a scale that reads 0.2 N when nothing hangs from it. Not fixed by averaging.
pound (lb)
An imperial unit. As a mass, 1 lb = 0.4536 kg. As a force (pound-force), 1 lb ≈ 4.45 N.
Your turn to be the scientist
So far you have followed other people's experiments. In this lesson you will design your own. The skills are the same ones physicists, engineers and kinesiologists use every day: ask a precise question, make a prediction based on theory, run a fair test, and decide honestly whether the evidence supports the prediction.
A model plan: does friction depend on the normal force?
1. Question. How does the kinetic friction on a wooden block sliding on a lab bench depend on the normal force? Does it depend on the contact area?
2. Hypothesis. If the normal force is doubled, then the kinetic friction will double, because Ff,k = μk FN with μk constant for the same surfaces. If the block is turned onto a smaller face, then friction will stay about the same, because friction does not depend on contact area.
3. Variables.
- Independent: normal force (add 500 g masses on top of the block).
- Dependent: kinetic friction (force-sensor reading while the block slides at constant speed).
- Controlled: same block, same face (for part 1), same section of bench, horizontal pull, slow constant speed.
4. Procedure (summary). Measure the mass of the block. Attach the force sensor and pull horizontally at a slow, steady speed. Record the average reading during steady sliding. Repeat 3 times. Add 500 g and repeat, up to 2.0 kg added. Then repeat one trial set with the block on its side.
5. Safety. Keep masses from falling off the bench (feet!), pull gently, and clean up promptly.
6. Prediction using Newton's laws. At constant speed, Fnet = 0, so the sensor's pull equals kinetic friction (FBD: Fpull forward = Ff backward; FN = Fg).
| Total mass (kg) | FN (N) | Trial 1 (N) | Trial 2 (N) | Trial 3 (N) | Average Ff,k (N) |
|---|
| 0.50 | 4.9 | 1.5 | 1.7 | 1.6 | 1.6 |
| 1.00 | 9.8 | 3.1 | 2.9 | 3.0 | 3.0 |
| 1.50 | 14.7 | 4.5 | 4.7 | 4.6 | 4.6 |
| 2.00 | 19.6 | 6.1 | 5.9 | 6.0 | 6.0 |
| 2.50 | 24.5 | 7.4 | 7.6 | 7.5 | 7.5 |
Worked exampleExample 1: Analysing the data
Use the sample data. (a) Graph Ff,k against FN and find μk. (b) Does the evidence support the hypothesis? (c) When the block was turned on its side (FN = 9.8 N), the average friction was 3.1 N. What does that show?
- (a) The points lie close to a straight line through the origin. Points on the best-fit line: (0, 0.1) and (24.5, 7.5) approximately. Slope ≈ (7.5 − 0.1) ÷ 24.5 ≈ 0.30. Since Ff,k = μk FN, the slope is μk ≈ 0.30.
- (b) Doubling FN from 9.8 N to 19.6 N doubled Ff,k from 3.0 N to 6.0 N. The relationship is linear and proportional, so the evidence supports the first hypothesis.
- (c) 3.1 N compared with 3.0 N on the large face: a difference of about 3%, within the scatter between trials (±0.1 N). So friction does not depend noticeably on contact area, supporting the second hypothesis.
μk ≈ 0.30; friction is proportional to the normal force and independent of contact area, within experimental error.
Friction against normal force for the drag sled. The points fall close to a straight line through the origin, so friction is proportional to FN, and the slope is μk.Units, precision and errors
SI and imperial units. Physics uses SI units (kg, m, s, N), but many Canadian products still show imperial units. Luggage scales and some bathroom scales read in pounds (lb), and some tire gauges and car specifications use imperial units too.
- Mass: 1 lb = 0.4536 kg (so 10 lb ≈ 4.5 kg).
- Force (pound-force): 1 lb ≈ 4.45 N.
- Speed: 1 mile per hour (mph) ≈ 1.61 km/h ≈ 0.447 m/s.
Precision. Record every reading to the precision of the instrument, e.g. 3.1 N on a sensor that reads to 0.1 N, and keep that many significant digits in answers.
Errors. Random errors (jerky pulling, reading a moving needle) are reduced by repeating and averaging. Systematic errors (a sensor not zeroed, pulling at an angle instead of horizontally) shift every result; repeat trials do not fix them, so check and zero your instruments first.
Communicating. A lab report includes: title, question, hypothesis, materials, procedure (numbered steps), FBD, data table, graph, calculations, conclusion (does the evidence support the hypothesis?), evaluation (sources of error and improvements).
Worked exampleExample 2: Converting imperial readings
A student drags a box with a luggage scale that reads in pounds. While the box slides steadily, the scale reads 3.5 lb. The box and its contents have a mass of 12 lb. Find the kinetic friction in newtons and μk.
- Friction (force): 3.5 lb × 4.45 N/lb ≈ 15.6 N.
- Mass: 12 lb × 0.4536 kg/lb ≈ 5.44 kg. FN = 5.44 × 9.8 ≈ 53.3 N.
- μk = 15.6 ÷ 53.3 ≈ 0.29.
- Shortcut check: because both readings are in lb, μk = 3.5 ÷ 12 ≈ 0.29 too. A luggage scale in "lb" reads pound-force, and 1 lb of mass weighs 1 lb of force on Earth.
Just for funIn 1999, NASA lost the Mars Climate Orbiter partly because one team's software produced numbers in imperial units (pound-force seconds) while another team's expected SI units (newton seconds). Moral: write your units on every number, even in a lab notebook.
Hands-on activityPlan and run your own forces inquiry
Choose one question (or invent your own, and check it with a parent or teacher):
- Does the kinetic friction on a shoe depend on the type of sole (running shoe, winter boot, dress shoe)?
- How does adding mass to a toy truck change how far it rolls after leaving the same ramp?
- Does the terminal velocity of a stack of coffee filters depend on the number of filters?
- Does friction depend on the surface (tile, wood, carpet) for the same shoebox sled?
Write a plan with: question; hypothesis (If..., then..., because...); independent, dependent and controlled variables; materials; numbered procedure; safety; a blank data table with units. Show it to a parent before you start.
Carry out at least 3 trials for each of at least 4 values of the independent variable. Graph your results, describe the pattern, and write a conclusion and evaluation (two sources of error, one improvement).
What to look for: a single variable changed at a time, units in table headings, averages, a labelled graph with a best-fit line, a conclusion that refers to the data.
Your turn
1Write a hypothesis for: "How does the mass of a cart affect its acceleration when pulled by a constant force?"
Sample: If the mass of the cart is doubled, then its acceleration will be halved, because Newton's second law says a = Fnet ÷ m.
2For the question above, name the independent, dependent and two controlled variables.
Independent: mass of the cart. Dependent: acceleration. Controlled (any two): pulling force, same track, level surface, same cart wheels.
3Why should you pull a drag sled at a constant speed when measuring kinetic friction?
At constant speed Fnet = 0, so the pulling force equals kinetic friction. If it were speeding up, the pull would be larger than friction.
4Convert 8.0 lb (mass) to kilograms.
5A force sensor reads 0.3 N when nothing is attached. What type of error is this, and how do you fix it?
A systematic error (zero offset). Zero the sensor before measuring, or subtract 0.3 N from every reading.
6Why repeat each trial three times?
To reduce the effect of random errors by averaging, and to see how consistent the results are.
More practice: warm-up
1What three parts does an "If..., then..., because..." hypothesis have?
The change you make, the predicted result, and the scientific reason.
2Which variable goes on the y-axis of a graph?
3Convert 10 lb of force to newtons.
A test where only one variable (the independent variable) is changed.
5Name one item that belongs in a lab report's evaluation.
Any one: sources of error, suggested improvements, how reliable the results are.
More practice: on your own
1A student's drag-sled data give a best-fit line Ff,k = 0.42 FN + 0.5. What is μk, and what might the 0.5 N intercept mean?
μk ≈ 0.42 (the slope). The 0.5 N intercept suggests a systematic error, such as an unzeroed sensor or pulling slightly upward or jerkily.
2Design a test to check whether kinetic friction depends on speed. Name the variables.
Pull the same sled over the same surface at several steady speeds (e.g. measured with a motion sensor). Independent: speed. Dependent: friction (sensor reading). Controlled: mass, surface, horizontal pull. Repeat each speed 3 times.
3A student pulled a sled at an upward angle instead of horizontally. Explain how this affects the measured μk.
Pulling upward lifts slightly on the sled, so FN is less than mg. Friction is smaller, but the student divides by mg, so μk comes out too small (and only part of the pull is horizontal, which also confuses the reading). This is a systematic error.
4A car's speed is 60 mph. Convert it to km/h and m/s.
60 × 1.61 ≈ 97 km/h; 60 × 0.447 ≈ 27 m/s.
5Two trials gave 4.6 N and 4.8 N, and a third gave 7.2 N. What should you do with the third value?
It is far from the others, so it is probably a mistake (an outlier: perhaps a jerky pull). Repeat the trial; if the redo agrees with 4.6 to 4.8 N, leave out 7.2 N and explain why in the report.
Challenge
1Plan an inquiry to measure g using a cart and hanging mass on a frictionless track (Atwood-style). Give the equation you would use and what you would graph.
For cart mass M and hanging mass m: a = mg ÷ (M + m). Keep the total mass M + m constant by moving masses from the cart to the hanger, measure a for each m with a motion sensor, and graph a against m/(M + m). The slope is g. Repeat trials; compare the slope with 9.8 m/s² (percent error).
2In the drag-sled data above, the friction on the block's small face was 3.1 N vs 3.0 N on the large face. A classmate concludes, "Smaller area gives more friction." Evaluate this conclusion.
The difference (0.1 N) is the same size as the trial-to-trial scatter (readings varied by about ±0.1 N), so it is not significant. The evidence shows friction is about the same for both faces. More trials, and testing on more surfaces, would strengthen the conclusion.
3Draw (describe) the vector diagram for the forces on the sled in Example 1 when it is pulled at constant speed, and explain how it shows Fnet = 0.
Place the force arrows tip to tail: pull forward (e.g. 3.0 N right), then friction back (3.0 N left), then Fg down (9.8 N) and FN up (9.8 N). The last arrow's tip ends at the starting point: the diagram closes, so the resultant (net force) is zero.
Quiz
1. In an investigation of how mass affects acceleration, the pulling force should be:
2. The best way to reduce random error is to:
3. A force sensor that reads 0.2 N with nothing attached causes:
5. A graph of kinetic friction against normal force is a straight line through the origin with slope 0.25. This means:
6. Which is the best hypothesis?
Big idea: Planning and conducting an inquiry into one-dimensional forces (C2.5), using friction coefficients (C2.4) and appropriate units and representations (A1.12).
How to help: Review your teen's plan before the investigation: Is only one thing changing? Are the measurements safe and possible with what you have at home? Is there a data table with units? Help time or record if needed, but let them do the analysis.
Common difficulties:
- Changing several variables at once.
- Hypotheses with no reason ("because" part missing).
- Mixing imperial and SI units in the same calculation.
- Conclusions that ignore the data or claim "proof". Scientists say the evidence supports (or does not support) a hypothesis.