Unit 04 - Grade 11-12 Physics

Dynamics and Newton's Laws

Move from describing motion to explaining why motion changes. Learn forces, Newton's laws, free-body diagrams, net force, mass, weight, normal force, tension, friction, and equilibrium.

Lesson roadmap

What Students Should Master in This Unit

Kinematics describes motion. Dynamics explains the cause of motion changes. This unit teaches students how to identify forces, draw free-body diagrams, calculate net force, and use Newton's laws to predict acceleration or unknown forces.

Identify forces

Recognize weight, normal force, friction, tension, applied force, spring force, and drag.

Draw force models

Use free-body diagrams to isolate one object and show only the forces acting on it.

Apply Newton's laws

Use net force to explain rest, constant velocity, acceleration, and interactions.

Quick navigation

Jump to a Topic

Force Basics Newton's Laws Free-Body Diagrams Net Force Mass and Weight Normal Force Tension Friction Equilibrium Lab Skills Worked Examples Practice Problems
Core idea

1. Force Basics

A force is a push or pull. Forces are vectors, so every force has magnitude and direction. The SI unit of force is the newton.

Force basics diagram Forces are pushes or pulls with direction push pull normal weight
Each force arrow should show the force direction and should be labeled with the interaction causing it.
Force unit 1 N = 1 kg·m/s2 One newton gives a 1 kg object an acceleration of 1 m/s2.
Net force Fnet = ΣF The vector sum of all forces on one object.
Dynamics link Fnet = ma Net force causes acceleration.

Common Forces

Force Symbol Direction When It Appears
WeightFg or WDownward, toward EarthAny object with mass near Earth.
Normal forceFN or NPerpendicular to a surfaceObject touches a surface.
FrictionfParallel to surface, opposes slipping or attempted slippingSurfaces interact with roughness.
TensionTAlong a rope, string, or cableObject is pulled by a rope.
Applied forceFappDirection of push or pullA person or device pushes or pulls.
Spring forceFsOpposes stretch or compressionSpring is stretched or compressed.
Air resistance or dragFdOpposes motion through fluidObject moves through air or liquid.
The foundation

2. Newton's Three Laws of Motion

Newton's laws overview diagram Newton's laws connect force, motion, and interactions 1. Inertia Fnet = 0 keeps motion unchanged 2. F = ma net force causes acceleration 3. Interaction pairs
First law: zero net force means no acceleration. Second law: net force causes acceleration. Third law: forces come in pairs on different objects.

Newton's First Law: Inertia

An object at rest stays at rest, and an object moving at constant velocity stays moving at constant velocity unless acted on by a nonzero net force.

Meaning: If Fnet = 0, acceleration is zero. The object may be at rest or moving at constant velocity.

Newton's Second Law: Net Force and Acceleration

The acceleration of an object depends on the net force and the mass of the object.

Fnet = ma

Acceleration points in the direction of the net force. A larger net force causes more acceleration. A larger mass causes less acceleration for the same net force.

Newton's Third Law: Interaction Pairs

When object A exerts a force on object B, object B exerts an equal-magnitude, opposite-direction force on object A.

Common mistake: Third-law forces act on different objects, so they do not cancel each other on the same free-body diagram.
Force modeling

3. Free-Body Diagrams

A free-body diagram is a simplified drawing that shows one object and all external forces acting on that object. It is the most important setup step in dynamics.

Free-body diagram example Draw only forces acting on the chosen object Fapp f FN Fg real object free-body diagram
A free-body diagram isolates one object and replaces all contacts or fields with force arrows.

How to Draw a Good Free-Body Diagram

  1. Choose the object you are analyzing.
  2. Represent the object as a dot or simple box.
  3. Draw only forces acting on that object.
  4. Draw each force as an arrow pointing in the correct direction.
  5. Label every force clearly.
  6. Choose axes that make the problem easier.
  7. Write a net-force equation for each direction.

Forces That Do Not Belong on a Free-Body Diagram

  • Forces the object exerts on other objects.
  • Velocity arrows, unless clearly labeled as motion and not force.
  • Acceleration arrows as if they were forces.
  • "Force of motion." Motion is not a force.
Exam habit: If the object is moving right, that does not automatically mean there is a force to the right. Check acceleration and interactions.
Vector sum

4. Net Force and Acceleration

The net force is the vector sum of all forces on an object. In one dimension, choose positive and negative directions, then add the signed forces.

Net force and acceleration diagram Unbalanced forces create acceleration 20 N 50 N Fnet = 30 N right acceleration points with net force
Forces in opposite directions subtract. The object accelerates in the direction of the net force.
Net force in x-direction ΣFx = max Use for horizontal motion or chosen x-axis.
Net force in y-direction ΣFy = may Use for vertical motion or chosen y-axis.
Acceleration a = Fnet / m Mass must be in kilograms.

Motion Conclusions

Net Force Acceleration Possible Motion
ZeroZeroRest or constant velocity.
NonzeroNonzeroSpeeding up, slowing down, or changing direction.
PositivePositiveAcceleration in the positive direction.
NegativeNegativeAcceleration in the negative direction.
Gravity and inertia

5. Mass and Weight

Mass and weight are related but not the same. Mass measures inertia. Weight is the gravitational force on an object.

Mass and weight diagram Mass measures inertia; weight is a force Earth: Fg = mg Moon: same mass, less weight m stays the same g changes by location
Mass is measured in kilograms. Weight is a gravitational force measured in newtons.
Weight Fg = mg Near Earth, g = 9.8 m/s2.
Mass unit kg Mass does not depend on location.
Weight unit N Weight changes when gravitational field strength changes.
Quantity Meaning Symbol Unit
MassAmount of matter and resistance to acceleration.mkg
WeightGravitational force on mass.Fg or WN
Surface contact

6. Normal Force

The normal force is a support force from a surface. It acts perpendicular to the surface. It is not automatically equal to weight in every situation.

Normal force diagram Normal force is perpendicular to the surface FN Fg FN Fg
On an incline, the normal force tilts with the surface and is not equal to the full weight.
Flat surface, no vertical acceleration FN = mg Only when no other vertical forces are present.
Vertical force equation ΣFy = may Use this to find normal force in general.
Incline preview FN = mg cos(θ) For a simple object on an incline with no other perpendicular acceleration.

When Normal Force Changes

  • A person pushes down on the object.
  • A person pulls upward on the object.
  • The object is in an accelerating elevator.
  • The object is on an inclined surface.
  • The surface is curved or the object is accelerating vertically.
Ropes and strings

7. Tension

Tension is a pulling force transmitted through a rope, string, cable, or chain. In many introductory problems, the rope is treated as massless and the tension is the same throughout the rope.

Tension force diagram Tension pulls along the rope T mg same T in ideal rope single hanging mass ideal rope model
Tension always pulls away from the object along the rope or cable.
Hanging object at rest T = mg Only if acceleration is zero.
Accelerating upward T - mg = ma Tension is greater than weight.
Accelerating downward mg - T = ma Tension is less than weight.
Model note: If a rope has mass, or if there is pulley friction, tension may not be the same everywhere. Most Grade 11-12 starter problems ignore these complications.
Surface resistance

8. Friction

Friction is a contact force parallel to a surface. It opposes slipping or the tendency to slip. There are two main types: static friction and kinetic friction.

Friction diagram Friction acts parallel to the surface motion or pull friction FN Fg
Kinetic friction opposes sliding. Static friction opposes the tendency to start sliding and adjusts up to a maximum.
Kinetic friction fk = μkFN Used when surfaces are sliding.
Maximum static friction fs,max = μsFN Maximum before slipping begins.
Static friction range fs ≤ μsFN Static friction adjusts up to a maximum.

Static vs. Kinetic Friction

Type When It Acts Direction Formula Idea
Static frictionSurfaces are not sliding relative to each other.Opposes intended slipping.Adjusts as needed up to fs,max.
Kinetic frictionSurfaces slide relative to each other.Opposes sliding motion.Usually equals μkFN.
Common mistake: Do not automatically set static friction equal to μsFN. That is only the maximum possible static friction.
Balanced forces

9. Equilibrium and Constant Velocity

An object is in equilibrium when the net force is zero. That means acceleration is zero. The object can be at rest or moving with constant velocity.

Equilibrium diagram Equilibrium means the vector sum of forces is zero FN Fg f Fapp ΣFx = 0 and ΣFy = 0
Equilibrium does not always mean rest. It means zero acceleration, so constant velocity is also possible.
Equilibrium condition ΣF = 0 No acceleration.
x-direction equilibrium ΣFx = 0 Horizontal forces balance.
y-direction equilibrium ΣFy = 0 Vertical forces balance.

Equilibrium Examples

  • A book resting on a table.
  • A sign hanging motionless from a cable.
  • A box being pulled across the floor at constant speed.
  • A person standing still in an elevator.
Investigation skills

10. Dynamics Lab Skills

Dynamics labs connect force measurements to acceleration. Students should be able to measure forces, calculate net force, make graphs, and compare experimental results to Newton's second law.

Dynamics lab setup diagram Dynamics labs test Fnet = ma with measurements force sensor a measured pull compare graph slope with mass or acceleration
Students should connect force sensor data, acceleration data, and graph slopes back to Newton's second law.

Common Dynamics Labs

  • Use a force sensor to measure applied force while pulling a cart.
  • Use a motion sensor to find acceleration from velocity-time data.
  • Investigate the relationship between net force and acceleration while mass stays constant.
  • Investigate the relationship between mass and acceleration while net force stays constant.
  • Measure coefficients of static and kinetic friction.
  • Test Newton's third law using two force sensors pulling on each other.

Graph Connections

Graph Meaning of Slope Physics Connection
Net force vs. accelerationMassFnet = ma
Acceleration vs. net force1/massAcceleration increases as net force increases.
Friction force vs. normal forceCoefficient of frictionf = μFN
Worked examples

11. Worked Examples

Example 1: Net force from two horizontal forces

A 12 kg box is pushed right with 80 N and pulled left by friction with 20 N. Find net force and acceleration.

Choose right as positive. Fnet = 80 N - 20 N = 60 N right.

a = Fnet/m = 60 N / 12 kg = 5.0 m/s2 right.

Example 2: Force needed for acceleration

A 6.0 kg cart accelerates at 2.5 m/s2. Find the net force.

Fnet = ma = (6.0)(2.5) = 15 N.

Example 3: Weight

Find the weight of a 70.0 kg person near Earth's surface.

Fg = mg = (70.0)(9.8) = 686 N downward.

Example 4: Kinetic friction

A 10.0 kg box slides across a horizontal floor. The coefficient of kinetic friction is 0.30. Find the kinetic friction force.

FN = mg = (10.0)(9.8) = 98 N.

fk = μkFN = (0.30)(98) = 29.4 N opposite motion.

Example 5: Hanging mass at rest

A 4.0 kg mass hangs motionless from a rope. Find the tension.

Motionless means a = 0, so forces balance.

T = mg = (4.0)(9.8) = 39.2 N upward.

Example 6: Elevator apparent weight

A 60.0 kg student stands on a scale in an elevator accelerating upward at 1.5 m/s2. Find the scale reading.

The scale reads normal force. Choose upward positive.

ΣFy = ma, so FN - mg = ma.

FN = m(g + a) = 60.0(9.8 + 1.5) = 678 N.

Independent practice

12. Practice Problems

Try each problem first. Draw a free-body diagram before calculating whenever forces are involved.

1. A 5.0 kg object has a net force of 20 N to the right. Find acceleration.

Answer

a = Fnet/m = 20/5.0 = 4.0 m/s2 right.

2. A 3.0 kg object accelerates at 6.0 m/s2. Find net force.

Answer

Fnet = ma = (3.0)(6.0) = 18 N.

3. Find the weight of a 12 kg object near Earth.

Answer

Fg = mg = (12)(9.8) = 117.6 N downward.

4. A 20 kg box rests on a level floor. Find the normal force.

Answer

With no vertical acceleration and no other vertical forces, FN = mg = 196 N upward.

5. A 15 kg box is pushed right with 90 N while friction acts left with 30 N. Find acceleration.

Answer

Fnet = 90 - 30 = 60 N right. a = 60/15 = 4.0 m/s2 right.

6. A 10 kg object slides with kinetic friction coefficient 0.20 on a horizontal surface. Find friction.

Answer

FN = mg = 98 N. fk = μkFN = (0.20)(98) = 19.6 N.

7. A 4.0 kg object hangs at rest from a rope. Find tension.

Answer

T = mg = (4.0)(9.8) = 39.2 N.

8. A 4.0 kg object hangs from a rope and accelerates upward at 2.0 m/s2. Find tension.

Answer

T - mg = ma, so T = m(g + a) = 4.0(9.8 + 2.0) = 47.2 N.

9. A 50 kg student stands on a scale in an elevator moving at constant velocity. Find the scale reading.

Answer

Constant velocity means a = 0. FN = mg = 50(9.8) = 490 N.

10. A 50 kg student is in an elevator accelerating downward at 2.0 m/s2. Find the scale reading.

Answer

Choose upward positive. FN - mg = m(-2.0).

FN = m(g - 2.0) = 50(7.8) = 390 N.

11. A box moves at constant speed while a 40 N force pulls right. What is the friction force?

Answer

Constant speed means net force is zero. Friction is 40 N left.

12. A maximum static friction force is 75 N. If a 50 N push is applied and the object does not move, what is static friction?

Answer

Static friction adjusts to match the push: 50 N opposite the push.

13. A 25 kg crate has FN = 245 N and μk = 0.15. Find kinetic friction.

Answer

fk = μkFN = (0.15)(245) = 36.8 N.

14. Two forces act on an object: 25 N east and 10 N west. Find net force.

Answer

Fnet = 25 - 10 = 15 N east.

15. A 2.0 kg object has forces 12 N right and 4 N left. Find acceleration.

Answer

Fnet = 8 N right. a = 8/2.0 = 4.0 m/s2 right.

16. A person pushes on a wall with 100 N. What force does the wall exert on the person?

Answer

100 N in the opposite direction. This is Newton's third law.

Final review

13. What to Know Before Moving On

  • Forces are vectors measured in newtons.
  • A free-body diagram shows only forces acting on one object.
  • Net force is the vector sum of all forces on an object.
  • If net force is zero, acceleration is zero.
  • Newton's second law is Fnet = ma.
  • Weight is Fg = mg and acts downward near Earth.
  • Normal force is perpendicular to the surface and is not always equal to weight.
  • Static friction adjusts up to a maximum; kinetic friction acts while surfaces slide.
  • Newton's third-law pairs act on different objects.
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