Newton’s Laws of Motion

Isaac Newton

Isaac Newton Smart Guy Liked Apples Invented Calculus Came up with 3 laws of

motion Named stuff after himself

Intertia

Inertia is how much an object resists a change in its velocity.

Measured by mass

1st Law

An object at rest stays at rest unless acted on by an external force. An object in motion continues to travel with constant velocity unless acted on by an external force.

Law of Inertia

2nd Law

The acceleration of an object is in the direction of the net external force acting on it. It is proportional to the net external force, and is inversely proportional to the mass of the object.

-- or --

3rd Law

When two objects interact they each exert a force on the other. These forces are equal in magnitude and opposite in direction.

Forces always occur in pairs

3rd Law

“Action-Reaction” forces never cancel out because they act on different objects.

Common Forces

Units

F = ma m is measured in kg a is measured in m/s2

F is measured in kg m/s2, called a Newton (N)

Gravity (Fg)

Acts at a distance (gravitational field)

Force due to Gravity = Weight Acceleration due to Gravity =

Constant g = 9.8 m/s2

Normal Force (FN)

Contact Force Acts perpendicular to the surface

Friction (Ff)

Contact force

Acts parallel to the surface

Acts opposite the direction of motion

Spring Force (Fs)

Contact force Acts opposite the

direction the spring is stretched or compressed

Proportional to stiffness of spring and how much it is stretched or compressed

Spring Force (Fs)

k = spring constant (N/m)

x = displacement from equilibrium (m)

negative shows direction

Tension (T)

Contact force Force exerted by a

string or rope Always acts along

the string or rope Equal on both

ends of the string or rope*

* Unless you have a pulley with mass, like in AP Physics

Friction

What is friction?

Friction is a resistive force caused by two surfaces sliding across each other.

Always acts opposite the direction of motion

Types of Friction

Static Friction - Fs

Friction force between two stationary surfaces.

Kinetic Friction – Fk

Friction force between two sliding surfaces.

Fs is always greater than Fk

Harder to start moving than to keep moving

Coefficient of Friction

Coefficient of friction describes how rough the surface is. Higher is rougher.

Denoted by the Greek letter mu (μ) pronounced “mew”

μs = coefficient of static friction μk = coefficient of kinetic friction μ is always positive, usually between

0 and 1.

Equation

Regardless of type (static or kinetic)

To find static friction, use μs

To find kinetic friction, use μk

Free Body Diagrams

Rules for FBDs

1. Draw the object and ALL forces acting ON the object

2. Draw and label all forces as vectors starting on the object and pointing the direction the force is acting

3. Draw and label the direction of acceleration as a vector that doesn’t touch the object

Box on Table

Draw the FBD for a box sitting at rest on a table.

FN

Fg

Box Being Pushed

Draw the FBD for a box being pushed across a rough table at a constant speed.

FN

Fg

FpushFf

v

Box Being Accelerated

Draw the FBD for a box being accelerated to the right across a rough table.

FN

Fg

FpushFf

a

Box Sliding Downhill

Draw the FBD for a box sliding down a rough hill.

F N

Fg

F f

a

Box Hanging from Rope

Draw the FBD for a box hanging from a rope.

T

Fg

Why?

FBDs are used to set up net force equations

Net force equations will be used to solve all Newton’s Laws problems.

Net Force Equations

2nd Law

For any individual force F = ma

For all forces on an object Fnet = ma Fnet = vector sum of all forces acting on

an object Separate Fnet equations for x and y

directions

Rules

For each object:1. Draw a Free Body Diagram2. Resolve forces at angles into x & y

components using sine and cosine3. Direction of acceleration is the positive

direction4. Write Fnet equations in x & y directions

5. Solve

Box Being Accelerated

x-direction

y-direction

FN

Fg

FpushFf

a

Box Pulled Up By Rope

x-direction

y-direction

T

Fg

a