Learning objectives
- I can explain and apply: Free-body diagrams.
- I can explain and apply: Newton's second law along an axis.
- I can explain and apply: Friction and normal force.
Greek Lyceum Grade 1 / Physics / Two-unit revision pilot
Forces and Newton's laws
Forces and Newton's laws: structured theory, worked examples, answered practice, and a mastery checklist for Greek Lyceum Grade 1.
CHAPTER PLAN
Learn, practise, and check your progress
Follow the steps in order or jump directly to the part you need.
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completed
Estimated active study time
156 minutes
1. Understand
Objectives, key ideas, and structured theory.
Open →2. Follow the method
Worked examples that explain every step.
Open →3. Practise
Graded tasks with hints and answer guidance.
Open →4. Consolidate
Assignments from core work to challenge.
Open →5. Check
A timed, marked test with solution guidance.
Open →
Progress is stored only in this browser and does not require AI credits.
Key ideas and checks
- ΣF=m·a, not one selected force=m·a.
- Acceleration is measured in m/s².
- An action–reaction pair does not imply equal accelerations.
Unit
Core theory
The essential chapter ideas in a clear sequence before practice.
Understanding the concept
First identify the body and draw its external forces. For constant mass in an inertial frame, resultant force equals m·a. Force changes velocity; the body need not already be moving in the force's direction.
Method and conditions
For vertical equilibrium, include weight, normal force and any other vertical forces with signs. The normal force equals mg only when the other vertical forces and vertical acceleration allow that equality.
Checking and coverage boundaries
During sliding, kinetic friction has magnitude μN and opposes relative sliding. Do not automatically use the same equality for static friction. After finding acceleration dynamically, use constant-acceleration kinematics if applicable.
Original pilot material — human educator review pending
Written specifically for YourFavTeacher with AI assistance, without copying past-paper prompts. Technical and numerical checks do not replace review by a human educator. It is not an official paper or endorsed by an examination body.
Physics
Worked examples
Follow the method step by step and check why every step is valid.
Worked example 1
A body of mass 5 kg experiences a horizontal resultant 15 N. Find acceleration.
- 1Newton's second law uses the resultant, not an arbitrary individual force.
- 2a=ΣF/m=15/5=3 m/s²
- 3Keep SI units and check the sign.
3 m/s²
Worked example 2
A 6 kg body starts from rest under constant resultant 12 N for 5 s. Find acceleration and final velocity.
- 1Connect dynamics and kinematics: a=ΣF/m, v=v₀+at.
- 2a=2 m/s²; υ=2·5=10 m/s
- 3Constant mass and resultant give constant acceleration.
a=2 m/s²; υ=10 m/s
Worked example 3
What resultant is required for acceleration 5 m/s² of a 6 kg body?
- 1Apply ΣF=ma in one inertial reference frame.
- 2ΣF=6·5=30 N
- 3The force points in the required acceleration direction.
30 N
Forces and Newton's laws
Practice with answers
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Core fluency6 minutes
A body of mass 2 kg experiences a horizontal resultant 6 N. Find acceleration.
Hint
Newton's second law uses the resultant, not an arbitrary individual force.
Answer guide
Newton's second law uses the resultant, not an arbitrary individual force. a=ΣF/m=6/2=3 m/s² Keep SI units and check the sign. 3 m/s²
Core fluency6 minutes
A body of mass 3 kg is pulled by 15 N and experiences opposing friction 6 N. Find acceleration.
Hint
Draw the two horizontal forces with opposite signs.
Answer guide
Draw the two horizontal forces with opposite signs. ΣF=15−6=9 N; a=9/3=3 m/s² Acceleration points in the resultant's direction. 3 m/s²
Core fluency6 minutes
A 2 kg body slides horizontally with μ=0.2 and g=10 m/s². There are no other vertical forces. Find kinetic friction.
Hint
Vertical equilibrium gives N=mg; then friction is μN.
Answer guide
Vertical equilibrium gives N=mg; then friction is μN. N=20 N; T=0.2·20=4 N Here μN describes kinetic friction, not static friction in general. 4 N
Application6 minutes
A constant resultant acts opposite the velocity. Does velocity immediately become zero?
Hint
Force determines acceleration, not an instantaneous reset of velocity.
Answer guide
Force determines acceleration, not an instantaneous reset of velocity. Velocity decreases gradually while acceleration opposes it. Stopping time depends on initial velocity and acceleration magnitude. No; a time interval is required.
Application6 minutes
A 3 kg body starts from rest under constant resultant 6 N for 2 s. Find acceleration and final velocity.
Hint
Connect dynamics and kinematics: a=ΣF/m, v=v₀+at.
Answer guide
Connect dynamics and kinematics: a=ΣF/m, v=v₀+at. a=2 m/s²; υ=2·2=4 m/s Constant mass and resultant give constant acceleration. a=2 m/s²; υ=4 m/s
Application6 minutes
A stationary 3 kg body on a horizontal table is pulled upwards by 6 N. With g=10 m/s², find the normal force while contact remains.
Hint
The upward pull reduces the normal force.
Answer guide
The upward pull reduces the normal force. N+6−30=0 ⇒ N=24 N The result is positive, consistent with contact. 24 N
Reasoning6 minutes
A small cart collides with a large cart: which exerts the larger force on the other at the same instant?
Hint
Newton's third law relates the forces in the same interaction.
Answer guide
Newton's third law relates the forces in the same interaction. Their magnitudes are equal and directions opposite. Accelerations may differ because the masses differ. Equal force magnitudes, not necessarily equal accelerations.
Reasoning6 minutes
What resultant is required for acceleration 2 m/s² of a 3 kg body?
Hint
Apply ΣF=ma in one inertial reference frame.
Answer guide
Apply ΣF=ma in one inertial reference frame. ΣF=3·2=6 N The force points in the required acceleration direction. 6 N
Common mistakes
- Omitting friction from the resultant.
- Always assuming N=mg.
- Cancelling action and reaction on the same body.
Mastery check
- I can solve independently and check: Free-body diagrams.
- I can solve independently and check: Newton's second law along an axis.
- I can solve independently and check: Friction and normal force.
Forces and Newton's laws
Chapter homework
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Core8 minutes
A body of mass 3 kg experiences a horizontal resultant 9 N. Find acceleration.
Hint
Newton's second law uses the resultant, not an arbitrary individual force.
Answer guide
Newton's second law uses the resultant, not an arbitrary individual force. a=ΣF/m=9/3=3 m/s² Keep SI units and check the sign. 3 m/s²
Core8 minutes
A body of mass 4 kg is pulled by 20 N and experiences opposing friction 8 N. Find acceleration.
Hint
Draw the two horizontal forces with opposite signs.
Answer guide
Draw the two horizontal forces with opposite signs. ΣF=20−8=12 N; a=12/4=3 m/s² Acceleration points in the resultant's direction. 3 m/s²
Stretch8 minutes
A 3 kg body slides horizontally with μ=0.2 and g=10 m/s². There are no other vertical forces. Find kinetic friction.
Hint
Vertical equilibrium gives N=mg; then friction is μN.
Answer guide
Vertical equilibrium gives N=mg; then friction is μN. N=30 N; T=0.2·30=6 N Here μN describes kinetic friction, not static friction in general. 6 N
Stretch8 minutes
A constant resultant acts opposite the velocity. Does velocity immediately become zero?
Hint
Force determines acceleration, not an instantaneous reset of velocity.
Answer guide
Force determines acceleration, not an instantaneous reset of velocity. Velocity decreases gradually while acceleration opposes it. Stopping time depends on initial velocity and acceleration magnitude. No; a time interval is required.
Challenge8 minutes
A 4 kg body starts from rest under constant resultant 8 N for 3 s. Find acceleration and final velocity.
Hint
Connect dynamics and kinematics: a=ΣF/m, v=v₀+at.
Answer guide
Connect dynamics and kinematics: a=ΣF/m, v=v₀+at. a=2 m/s²; υ=2·3=6 m/s Constant mass and resultant give constant acceleration. a=2 m/s²; υ=6 m/s
Challenge8 minutes
A stationary 4 kg body on a horizontal table is pulled upwards by 8 N. With g=10 m/s², find the normal force while contact remains.
Hint
The upward pull reduces the normal force.
Answer guide
The upward pull reduces the normal force. N+8−40=0 ⇒ N=32 N The result is positive, consistent with contact. 32 N
45 minutes / 40 marks
Full chapter test
A timed, full-mark self-assessment with model-answer guidance.
Show working, units and a final check. Equivalent correct methods are accepted. Timing is a revision guide, not official examination conditions.
1. A body of mass 4 kg experiences a horizontal resultant 12 N. Find acceleration.
5 marksAnswer guide
Newton's second law uses the resultant, not an arbitrary individual force. a=ΣF/m=12/4=3 m/s² Keep SI units and check the sign. 3 m/s²
2. A body of mass 5 kg is pulled by 25 N and experiences opposing friction 10 N. Find acceleration.
5 marksAnswer guide
Draw the two horizontal forces with opposite signs. ΣF=25−10=15 N; a=15/5=3 m/s² Acceleration points in the resultant's direction. 3 m/s²
3. A 4 kg body slides horizontally with μ=0.2 and g=10 m/s². There are no other vertical forces. Find kinetic friction.
5 marksAnswer guide
Vertical equilibrium gives N=mg; then friction is μN. N=40 N; T=0.2·40=8 N Here μN describes kinetic friction, not static friction in general. 8 N
4. A constant resultant acts opposite the velocity. Does velocity immediately become zero?
5 marksAnswer guide
Force determines acceleration, not an instantaneous reset of velocity. Velocity decreases gradually while acceleration opposes it. Stopping time depends on initial velocity and acceleration magnitude. No; a time interval is required.
5. A 5 kg body starts from rest under constant resultant 10 N for 4 s. Find acceleration and final velocity.
5 marksAnswer guide
Connect dynamics and kinematics: a=ΣF/m, v=v₀+at. a=2 m/s²; υ=2·4=8 m/s Constant mass and resultant give constant acceleration. a=2 m/s²; υ=8 m/s
6. A stationary 5 kg body on a horizontal table is pulled upwards by 10 N. With g=10 m/s², find the normal force while contact remains.
5 marksAnswer guide
The upward pull reduces the normal force. N+10−50=0 ⇒ N=40 N The result is positive, consistent with contact. 40 N
7. A small cart collides with a large cart: which exerts the larger force on the other at the same instant?
5 marksAnswer guide
Newton's third law relates the forces in the same interaction. Their magnitudes are equal and directions opposite. Accelerations may differ because the masses differ. Equal force magnitudes, not necessarily equal accelerations.
8. What resultant is required for acceleration 4 m/s² of a 5 kg body?
5 marksAnswer guide
Apply ΣF=ma in one inertial reference frame. ΣF=5·4=20 N The force points in the required acceleration direction. 20 N
Unit
Official sources and verification
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Physics
Learn force diagrams, axis choice, units, and the transition from physical picture to equation.
What this chapter covers
The structure follows the official textbook layout and is used to organise study.
Free-body diagrams
Newton's second law along an axis
Friction and normal force
Where to focus
The areas that usually create mistakes or need extra revision.
I can solve independently and check: Free-body diagrams.
I can solve independently and check: Newton's second law along an axis.
I can solve independently and check: Friction and normal force.
Sources, daily material, and resources
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Start from the official textbook or specification referenced on the subject page.
Use the notes and examples as support, not as a replacement for the official syllabus.
Check the current syllabus version before exam preparation.
Practice by subtopic
Targeted practice before full tests so coverage is clear.
A body of mass 2 kg experiences a horizontal resultant 6 N. Find acceleration.
A body of mass 3 kg is pulled by 15 N and experiences opposing friction 6 N. Find acceleration.
A 2 kg body slides horizontally with μ=0.2 and g=10 m/s². There are no other vertical forces. Find kinetic friction.
A constant resultant acts opposite the velocity. Does velocity immediately become zero?
A 3 kg body starts from rest under constant resultant 6 N for 2 s. Find acceleration and final velocity.
A stationary 3 kg body on a horizontal table is pulled upwards by 6 N. With g=10 m/s², find the normal force while contact remains.
A small cart collides with a large cart: which exerts the larger force on the other at the same instant?
What resultant is required for acceleration 2 m/s² of a 3 kg body?
Mocks and progress checks
How to measure progress in this chapter and when it enters a cumulative mock.
Start with untimed practice by subtopic.
Move to a short timed checkpoint only after completing the mastery checklist.
Record each error with the correct method and revisit it after 48 hours.
Next step
What to do after finishing the chapter and how it connects to the next unit.
Complete the practice without support.
Explain the core method aloud in under two minutes.
Continue to the next chapter or request targeted tutor support.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.