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Newton’s Laws of Motion
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Isaac Newton
Isaac Newton Smart Guy Liked Apples Invented Calculus Came up with 3 laws of
motion Named stuff after himself
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Intertia
Inertia is how much an object resists a change in its velocity.
Measured by mass
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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
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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 --
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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
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3rd Law
“Action-Reaction” forces never cancel out because they act on different objects.
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Common Forces
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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)
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Gravity (Fg)
Acts at a distance (gravitational field)
Force due to Gravity = Weight Acceleration due to Gravity =
Constant g = 9.8 m/s2
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Normal Force (FN)
Contact Force Acts perpendicular to the surface
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Friction (Ff)
Contact force
Acts parallel to the surface
Acts opposite the direction of motion
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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
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Spring Force (Fs)
k = spring constant (N/m)
x = displacement from equilibrium (m)
negative shows direction
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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
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Friction
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What is friction?
Friction is a resistive force caused by two surfaces sliding across each other.
Always acts opposite the direction of motion
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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
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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.
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Equation
Regardless of type (static or kinetic)
To find static friction, use μs
To find kinetic friction, use μk
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Free Body Diagrams
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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
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Box on Table
Draw the FBD for a box sitting at rest on a table.
FN
Fg
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Box Being Pushed
Draw the FBD for a box being pushed across a rough table at a constant speed.
FN
Fg
FpushFf
v
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Box Being Accelerated
Draw the FBD for a box being accelerated to the right across a rough table.
FN
Fg
FpushFf
a
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Box Sliding Downhill
Draw the FBD for a box sliding down a rough hill.
F N
Fg
F f
a
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Box Hanging from Rope
Draw the FBD for a box hanging from a rope.
T
Fg
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Why?
FBDs are used to set up net force equations
Net force equations will be used to solve all Newton’s Laws problems.
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Net Force Equations
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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
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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
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Box Being Accelerated
x-direction
y-direction
FN
Fg
FpushFf
a
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Box Pulled Up By Rope
x-direction
y-direction
T
Fg
a
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