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.
Vector Addition: The process of combining vectors; added tip to tail.
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=(v_f-v_i)/t
d=v_it+at²/2
v_f²=v_i²+2ad
acceleration due to gravity = -9.8 m/s²
Pythagorean Theorem:  c²=a²+b²
Sin θ = opp/hyp
Cos θ = adj/hyp
Tan θ = opp/adj
Fnet=ma
μ=Ff/FN
F_net=ΣF = the sum of all forces

Variables Used

v= velocity (usually average velocity or constant velocity)
a=acceleration
F= force
F_f=frictional force
F_N=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 : F_net= 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= ?
F_net= ?

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.
F_net=ΣF =100N-29.4N=70.6N

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