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C2.5 · Plan an inquiry into one-dimensional forces

Learn to plan an inquiry into one-dimensional forces through clear examples and targeted practice.

Ontario Grade 11 Physics

Forces

From a clear question to useful, safe evidence

A force is a push or pull. In this lesson, one-dimensional means that the forces and motion being studied lie along one straight line. An inquiry is a planned investigation that uses observations or measurements to answer a question. Planning comes before collecting data: a prediction or sample calculation is not a measurement. We will use familiar science skills—choosing variables, controlling conditions, recording units, and repeating measurements—to make a force inquiry clear and fair.

What you will learn

Turn a one-dimensional force situation into a testable inquiry question.
Identify the system, direction, variables, equipment, and safety steps before collecting evidence.
Use a free-body diagram and the net-force model to plan measurements.
Distinguish planned procedures and predicted values from evidence actually measured.

1. Bridge from motion and measurement

A scalar has size only. Mass, time, and distance are scalars. A vector has both size and direction. Force and displacement are vectors. In a one-dimensional inquiry, choose one line and describe vector directions along that line.

A system is the object or group of objects you choose to study. For example, the system might be a cart alone, or a cart and its attached load. State this choice because the forces acting on the system depend on what is included.

A reference frame is the point of view used to describe position and motion. For a classroom cart investigation, the laboratory floor is a useful reference frame. Choose a positive direction, such as right along the track. Forces to the right are positive; forces to the left are negative. The choice is arbitrary, but it must remain consistent.

Force is measured in newtons, written

\mathrm{N}

. Mass is measured in kilograms, written

\mathrm{kg}

. Acceleration is measured in metres per second squared, written

\mathrm{m/s^2}

. A free-body diagram shows the chosen system and the forces acting on it. Each force arrow points in its force direction and is labelled.

F_{\text{net}}=ma

Name the system and reference frame before planning measurements.
Choose and label a positive direction.
A negative force value means the force points opposite to the chosen positive direction.

2. Build a testable plan

A useful inquiry question names what will be changed and what will be measured. For example: How does the net force on a cart affect the cart’s acceleration when the cart’s total mass is kept the same? This question is about one-dimensional forces if the cart moves along a straight track and the forces being compared act along that track.

The independent variable is the factor deliberately changed. The dependent variable is the result measured. Controlled variables are conditions kept the same so that the comparison is fair. In the example, net force is the independent variable, acceleration is the dependent variable, and total cart mass and track setup are controlled variables.

The model for planning is

F_{\text{net}}=ma

. Here,

F_{\text{net}}

is the vector total of the forces along the chosen line,

m

is the system’s mass, and

a

is its acceleration. With right positive, a force to the left has a negative value. The equation helps identify what needs to be measured or held constant. It does not supply experimental evidence.

Plan equipment that can measure the quantities your question requires. A force sensor or spring scale may measure force; a balance may measure mass; and a motion sensor or recorded positions at known times may be used to determine acceleration. Follow the equipment instructions and record each reading with its SI unit. If acceleration is calculated from motion data, state the method and keep the recorded positions and times as the original evidence.

Write a procedure in a repeatable order. Describe how the system will be set up, how the independent variable will be changed, how the dependent variable will be measured, and which conditions will stay fixed. Plan several different settings and repeat each one. Repeats help show whether a result is consistent; they do not guarantee that every source of uncertainty has been removed.

F_{\text{net}}=ma

State a question that can be answered with measurements.
Identify independent, dependent, and controlled variables.
Plan equipment, a repeatable procedure, units, and repeated trials.
Keep predicted values separate from observations.

3. Use diagrams, records, and checks

Draw a free-body diagram for the system. For a cart pulled to the right on a level track, the horizontal pull points right. Friction, if present, points opposite the cart’s motion or tendency to move. The vertical forces include gravity downward and the support force from the track upward. If the question concerns only forces along the track, label the horizontal direction clearly and explain which forces are included in the net force for that direction.

A good data table has headings with units. Leave blank spaces for measurements until the inquiry is actually carried out. Record the direction of each force as well as its size. A later calculation can use signed values, with the chosen positive direction stated at the top of the table.

Before collecting evidence, check whether the plan answers the question. Can the changed variable actually be changed? Can the outcome be measured with the available equipment? Are important conditions controlled? Could a force act in an unintended direction? Is the procedure safe? These checks can lead to a better plan without pretending that the inquiry has already happened.

A simulation can help explore a proposed setup, but simulation output is not a physical measurement. Identify it as simulated output if used. Likewise, a predicted value calculated from a model is a prediction, not a measured result.

F_{\text{net}}=\sum F_i

Make diagram arrows agree with the positive direction.
Record evidence with units and direction.
Review fairness, measurement, safety, and repeatability before starting.

Planning record for a one-dimensional force inquiry

Planning item	Cart inquiry example
System and positive direction	Cart and attached load; right along track is positive
Independent variable	Net force along the track
Dependent variable	Cart acceleration along the track
Controlled condition	Total system mass
Evidence to record	Measured force and motion readings, with units and direction
Before starting	Check repeatability, equipment, controlled conditions, and safety

Worked example

Plan a cart-force inquiry

Plan an inquiry question and identify its variables for a cart on a straight track. Keep the cart’s total mass fixed and investigate different net forces along the track.

Set the system and direction
Choose the cart and any load attached to it as the system. Use the track as the one-dimensional line and the floor as the reference frame. Define right along the track as positive.
Choose the question and variables
Ask how changing the net force affects the cart’s acceleration. The independent variable is net force, the dependent variable is acceleration, and the controlled variable is total system mass. Keep the same track and measurement method for each setting.
Plan measurement and evidence
Use a force sensor to measure the applied force and a motion sensor to measure the cart’s motion. Plan repeated trials at each force setting. Record measured force in newtons and mass in kilograms; determine acceleration in metres per second squared using the stated motion-measurement method. These are planned measurements, not results.

Answer: A suitable plan investigates how measured net force relates to measured acceleration for a fixed-mass cart moving along a straight track.

Check: The question is one-dimensional, names a changed and measured quantity, and distinguishes planned measurements from evidence already collected.

Worked example

Use a prediction to choose force settings

For a proposed setup, a cart system has a mass of

0.80\,\mathrm{kg}

. The plan aims for an acceleration of

0.50\,\mathrm{m/s^2}

to the right. Find the net force target to guide the equipment setup. This is a prediction, not a measured result.

Define the system and direction
The system is the cart and attached load. Use the track as the line of motion, with right positive. The target acceleration is therefore positive.
Apply the model
Use the net-force relationship. The mass is in kilograms and acceleration is in metres per second squared, so their product gives force in newtons.
$F_{\text{net}}=ma$
Substitute with units
Multiply the planned mass by the target acceleration. Keep the units in the substitution so the result can be checked.
$F_{\text{net}}=(0.80\,\mathrm{kg})(+0.50\,\mathrm{m/s^2})=+0.40\,\mathrm{N}$

Answer: The setup target is

0.40\,\mathrm{N}

to the right, reported to two significant figures.

Check: The units reduce to newtons because

\mathrm{kg\cdot m/s^2}=\mathrm{N}

. The positive sign means right. A modest acceleration of a less-than-one-kilogram system calls for a modest force, so the target is reasonable. It must not be reported as a measured force.

Worked example

Plan a force-balance comparison

A proposed inquiry uses two horizontal pulls on a low-friction cart: a planned

1.20\,\mathrm{N}

pull to the right and a planned

0.70\,\mathrm{N}

pull to the left. Find the predicted horizontal net force and explain how it guides the plan.

Define the system and sign convention
The system is the cart. Use the straight track as the line and define right as positive. The leftward pull must therefore be assigned a negative sign.
Add the signed forces
Forces along one line combine by adding their signed values. This calculation predicts the net force for the proposed settings; it is not evidence from a trial.
$F_{\text{net}}=(+1.20\,\mathrm{N})+(-0.70\,\mathrm{N})=+0.50\,\mathrm{N}$
Use the prediction in the plan
The predicted result points right. Arrange and label the force sensors so that both directions can be recorded, and plan to compare the measured forces with the motion measurement. Repeat the setup and record actual readings only after carrying out the inquiry.

Answer: The predicted horizontal net force is

0.50\,\mathrm{N}

to the right, to two significant figures.

Check: Both terms are in newtons, so the result is in newtons. The larger pull is rightward, and the difference is

0.50\,\mathrm{N}

, so a rightward net force is reasonable. The value remains a prediction until measured.

Common mistakes and how to avoid them

Writing that the cart was measured to accelerate when the lesson only describes a proposed setup.

Correction: Label a calculated value as a prediction and reserve measured evidence for readings actually collected.

Adding force magnitudes without considering direction.

Correction: Choose a positive direction and give forces in the opposite direction negative signs before adding.

Changing the cart mass while also changing the applied force, then attributing the whole effect to force.

Correction: Identify controlled variables in advance. Keep the total mass fixed when studying the effect of changing net force.

Recording numbers without units or leaving out repeated trials.

Correction: Label every table heading with units, record direction where needed, and plan repeats to check consistency.

Lesson summary

An inquiry plan begins by naming the system, reference frame, and positive direction.
A testable question identifies what will change and what will be measured.
Use a free-body diagram and $F_{\text{net}}=ma$ to guide the plan and make predictions.
Keep controlled conditions consistent, choose suitable equipment, plan repeats, and record SI units and directions.
Predictions and simulation output are not physical measurements.

Check your understanding

Question 1

A student defines right as positive. A horizontal force of

0.40\,\mathrm{N}

points left. What signed value should be recorded?

$+0.40\,\mathrm{N}$
$-0.40\,\mathrm{N}$
$0.40\,\mathrm{kg}$
$0.40\,\mathrm{m/s^2}$

Show answer and explanation

-0.40\,\mathrm{N}

Left is opposite the chosen positive direction, so the force is recorded as

-0.40\,\mathrm{N}

Question 2

A plan changes net force while keeping the system’s mass fixed. Which quantity is the dependent variable in a question about the resulting motion?

The net force setting
The system’s mass
The measured acceleration
The direction chosen as positive

Show answer and explanation

The measured acceleration

Acceleration is the outcome measured in response to changing net force. The mass is controlled, and the force setting is changed.

Question 3

A student calculates a target force before using the equipment. How should that value be described?

As measured evidence
As a prediction for planning
As a repeated trial
As a simulation measurement

Show answer and explanation

As a prediction for planning

A value calculated before collecting readings is a prediction. It does not become measured evidence unless the force is actually measured.

Key terms

Inquiry: A planned investigation that uses observations or measurements to answer a question.
System: The object or group of objects chosen for study.
Reference frame: The viewpoint used to describe position and motion.
Scalar: A quantity with size but no direction.
Vector: A quantity with both size and direction.
Net force: The combined effect of the forces acting on a system, including their directions.
Free-body diagram: A drawing that shows the chosen system and the forces acting on it.
Independent variable: The factor deliberately changed in an inquiry.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation C2.5. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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