Balanced Forces and Newton's First Law
Key idea: Use one-body force diagrams and resultants to explain rest and constant velocity with Newton's first law.
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The core idea
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Learning objectives
- Distinguish contact forces from non-contact forces
- State that mass measures the amount of matter in a body
- Describe a gravitational field as a region where a mass experiences gravitational force
- Define gravitational field strength as gravitational force per unit mass
- Apply weight = mass × gravitational field strength
- Distinguish mass from weight
- Describe the effect of balanced and unbalanced forces on a body
- Describe ways a force may change motion
- Identify action–reaction pairs on interacting bodies
- Draw free-body diagrams for force systems in at most two dimensions
- Solve three-force static equilibrium graphically
- Apply resultant force = mass × acceleration
- Relate mass to resistance to change in motion
- Explain the effects of friction on motion
- Describe falling with and without air resistance, including terminal velocity
- Describe a moment as a force's turning effect in everyday examples
- Apply moment = force × perpendicular distance from the pivot
- State the principle of moments for a body in equilibrium
- apply the principle of moments to new situations or to solve related problems
- show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity
- Explain qualitatively how centre-of-gravity position affects stability
Retrieve: isolate one body
Before using Newton’s first law, sketch the free-body diagram of a book resting on a table. Include only external forces on the book. Check your force selection in Free Body Diagrams if needed.
The forces are Earth’s gravitational force on the book (weight) downward and the table’s normal force on the book upward. Do not add motion or resultant as extra forces.
One body, one resultant
Forces on a body are balanced when their vector resultant is zero:
Fᵣₑₛᵤₗₜₐₙₜ = 0 ⇒ a = 0.
Newton’s first law says that the selected body therefore remains at rest or continues with constant velocity. Constant velocity means constant speed in a straight line. A body moving around a curve changes direction, so it is accelerating even if its speed is constant.
Balanced forces: velocity does not change
Velocity–time graph examples for balanced forces: at rest (v = 0) and constant non-zero velocity.
Scroll across the graph to read all labels.
View figure data
| Time (s) | At rest | Constant velocity |
|---|---|---|
| 0 | 0 | 5 |
| 8 | 0 | 5 |
Modelled example: box at rest
Modelled example 1
A box at rest on a table
Problem
Study the worked solution
Select the body
Method
Analyse the box only.Reason
Its vertical forces are weight down and normal force up.Working
Take upward as positive: Fᵣₑₛᵤₗₜₐₙₜ = N-24.Use zero acceleration
Method
Set the resultant to zero.Reason
The box remains at rest.Working
N-24 = 0, so N = 24 N upward.
Guided practice: constant velocity
Guided practice 2
A cart moves without changing velocity
Problem
Use velocity before force
Hints
Hint 1: translate motion
Hint 2: balance components
View solution step by step
Apply Newton's first law
Method
Use a = 0, so Fᵣₑₛᵤₗₜₐₙₜ = 0.Reason
A moving body does not need a forward resultant to keep moving.Working
The driving force is 5.0 N east and the resultant is 0 N.
Misconception repair
- “It moves forward, so the resultant is forward.” No. The direction of velocity does not determine the resultant. Only changing velocity requires a resultant.
- “Balanced means no forces act.” No. Several real forces may act and add vectorially to zero.
- “Constant speed means balanced.” Only if direction is also constant. Uniform circular motion has changing velocity.
Changed-context transfer
Challenge 3
A parachutist at terminal velocity
Problem
Analyse the parachutist only
Hints
Hint 1: translate motion
Hint 2: balance the body
View solution step by step
Balance the vertical forces
Method
Air resistance is 720 N upward.Reason
The two forces on the parachutist give zero resultant.Working
Acceleration is zero, so the downward velocity remains constant.
Independent evidence
Without hints, analyse a train moving east around a curve at constant speed. Decide whether the resultant is zero and justify your answer using velocity rather than speed alone. Then compare it with the straight-track constant-velocity cart above.
Check your reasoning
The train’s velocity changes direction, so it accelerates and its resultant is not zero. The straight-track cart has constant velocity, zero acceleration and zero resultant.
Next, practise separating one-body resultants from cross-body interaction pairs in Newton’s Third-Law Interaction Pairs.
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Course and syllabus information
- Course
- SEC G3 Physics
- Edition
- SEC G3 Physics 2027