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Newton’s Laws Study Guide

Key Physics Terms

Vector: A quantity that represents magnitude (size) and direction.  It is usually represented with an arrow to indicate the appropriate direction.  They may or may not be drawn to scale.
Resultant: the result of adding two or more vectors; vector sum.
Vector Component: the parts into which a vector can be separated and that act in different directions from the vector.
Static Equilibrium:  A motionless state where all the forces acting on an object yield a net force of zero.
Dynamic Equilibrium: A condition of constant motion/zero acceleration where all the forces acting on an object yield a net force of zero.
Friction Force:  A force that acts to resist motion of objects that are in contact.
Normal Force: Support force that acts perpendicular to a surface.  If the surface is horizontal, this force balances the weight of the object.
Force: A vector quantity that tends to accelerate an object; a push or a pull.
Net Force, Fnet: : A combination of all the forces that act on an object

Key Formulas

v=d/t
a = Δv/Δt=(vf-vi)/t
d=vit+at2/2
acceleration due to gravity = -9.8 m/s2
Pythagorean Theorem:  c2=a2+b2
Sin θ = opp/hyp
Fnet=ma
μ=Ff/FN
Fnet=ΣF = the sum of all forces

Variables Used

v= velocity (usually average velocity or constant velocity)
a=acceleration
F= force
Ff=frictional force
FN=normal force
Δ= change in
θ= angle
m=mass
μ=coefficient of friction

Vector Diagram Static vs. Dynamic Equilibrium

• In static equilibrium, the net force on an object is zero; the object is also stationary.  The forces balance out to leave the object motionless.
• In dynamic equilibrium, the net force on an object is zero; however, the object is still moving at a constant velocity.  The forces balance out to leave the object in its current state of motion with no accelerations or changes.

Typical Key Metric Units

• Acceleration: m/s2, m/s/s
• Time: seconds, s
• Force: Newtons, N
• Mass: kilograms, kg
• Coefficient of friction: no units

Newton’s Laws

• Newton’s 1st law :  An object at rest wants to stay at rest, an object in motion tends to stay in motion; inertia.
• Newton’s 2nd law : Fnet= ma.
• Newton’s 3rd law:  For every force that is an equal and opposite force; action and reaction.

Newton’s Laws Problem Solving Tips

• These tips will make it easier to solve any force related physics problems.
• Thoroughly read the entire problem.
• Draw a diagram if needed.  Include a diagram to show all forces acting on a particular body.
• Identify all given information.
• Identify the quantity to be found.
• Select appropriate formula(s) that incorporate what you know and what you want to find.
• Convert units if needed.  Use units throughout your calculations.
• Do any mathematical calculations carefully.

Typical Dynamics Problem

Example:  A model rocket of mass 3 kg has an engine that produces 100N of upward thrust/force.  What is the resulting acceleration of the model rocket when it is fired.  Assume its mass is constant throughout its motion.  Ignore any frictional forces.

Given information:
Mass = 3 kg
Upward force = 100N

Unknown
acceleration= ?
Fnet= ?

First, find the weight of the rocket:
Although the mass is known, that isn’t the same as its weight.
Using  F=ma   Weight = 3kg (-9.8m/s2)=-29.4N

Second, find the net force on the rocket:
Our upward force is considered positive, the weight negative.
Fnet=ΣF =100N-29.4N=70.6N

Lastly, solve for the acceleration:
Use Fnet=ma   70.6N=3kg(a)       a=23.5m/s2