4bNewton's Second Law
Explore F = ma — how net force, mass, and acceleration are related, and how to solve real problems with free-body diagrams.
Newton's Second Law is the most used equation in classical mechanics. It lets engineers calculate the forces needed to accelerate vehicles, design safe structures, and predict the motion of everything from baseballs to rockets.
Lesson Overview
Newton's Second Law states that the net force on an object equals its mass times its acceleration: F = ma. This lesson covers how to calculate net force from multiple forces, how to draw free-body diagrams, and how friction and normal forces affect motion.
Key Concepts
F = ma
Net force equals mass times acceleration
Net Force
Vector sum of all forces acting on an object
Free-Body Diagrams
Arrows showing all forces on an isolated object
Normal Force
Perpendicular contact force from a surface
Friction Force
Opposes relative motion between surfaces
Units
Force in Newtons (N = kg·m/s²)
A 5 kg box is pushed with a net force of 20 N. What is its acceleration?
A 10 kg object accelerates at 3 m/s². What net force acts on it?
Two forces act on a 4 kg cart: 18 N to the right and 6 N to the left. Find the acceleration.
A 60 kg person stands on a scale in an elevator accelerating upward at 2 m/s². What does the scale read? (g = 10 m/s²)
A 3 kg block is pushed with 15 N across a surface with 6 N of friction. Find the acceleration.
A 8 kg object has a net force of 40 N applied to it. What is its acceleration?
Hint: Rearrange F = ma to solve for a.
A car of mass 1200 kg accelerates at 2.5 m/s². What net force does the engine provide?
Hint: Apply F = ma directly.
Three forces act on a box: 20 N right, 8 N left, and 4 N left. What is the net force and its direction?
Hint: Add forces in each direction, then find the difference.
A 70 kg person stands on a scale in an elevator moving downward at constant speed. What does the scale read? (g = 10 m/s²)
Hint: Constant speed means zero acceleration — what does that tell you about net force?
A 2 kg block is pushed with 10 N but friction exerts 4 N opposing motion. Draw a free-body diagram and find the acceleration.
Hint: Draw all forces as arrows, find net force, then use F = ma.
Key Vocabulary
Newton's Second Law
The net force on an object equals its mass multiplied by its acceleration (F = ma).
Example: Pushing a 2 kg cart with 10 N net force gives it an acceleration of 5 m/s².
Free-Body Diagram
A diagram showing an isolated object with all forces acting on it represented as labeled arrows.
Example: A free-body diagram of a falling ball shows only the downward weight arrow (ignoring air resistance).
Normal Force
The contact force exerted by a surface perpendicular to the surface on an object resting on it.
Example: A book on a table experiences a normal force equal to its weight, directed upward.
Friction Force
A force that opposes the relative motion or tendency of motion between two surfaces in contact.
Example: Sliding a box across the floor is opposed by kinetic friction acting backward on the box.
Interactive Practice — 5 Questions
A 6 kg object experiences a net force of 24 N. What is its acceleration?
If the mass of an object doubles while the net force stays the same, what happens to the acceleration?
Which diagram correctly represents all forces on a book resting on a table?
A 5 kg box is pushed with 30 N while friction exerts 10 N. What is the acceleration?
What are the SI units of force?
Independent Practice
A 12 kg object accelerates at 5 m/s². Calculate the net force acting on it.
A net force of 45 N acts on an object, giving it an acceleration of 9 m/s². What is the object's mass?
Draw a free-body diagram for a 3 kg block being pushed across a rough floor with 20 N applied force and 8 N friction. Calculate the acceleration.
A 1500 kg car brakes with a net force of 6000 N. What is the magnitude of its deceleration?
★ A 70 kg person rides an elevator. Calculate the scale reading when: (a) the elevator is at rest, (b) accelerating upward at 3 m/s², and (c) accelerating downward at 3 m/s². Use g = 10 m/s². Explain why the readings differ.
ChallengeCommon Mistakes
Using total force instead of net force in F = ma.
Always find the vector sum (net force) of all forces before applying F = ma. Forces in opposite directions subtract.
Forgetting that friction always opposes the direction of motion.
Friction acts opposite to the direction of motion (or intended motion). Subtract it from the applied force to find net force.
Thinking the normal force always equals mg.
Normal force equals mg only on a horizontal surface with no vertical acceleration. In an accelerating elevator, N ≠ mg.
Math Tips
The three forms of Newton's Second Law: F = ma, a = F/m, m = F/a. Identify which quantity is unknown and rearrange accordingly. Always use net force, not a single applied force.