Framework for Solving Force Problems
AP Physics 1 and AP Physics C: Mechanics
Newton’s First Law
An object will maintain its state of motion (or state of rest) unless acted on by an external unbalanced net force.
#=𝟎
!𝑭
" = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕
𝒗
In these problems you are looking for situations in which the object is at rest or who’s velocity is not changing. Be careful, a car moving at
20 mph but traveling around a corner wouldn’t qualify since its velocity is changing direction.
Newton’s Second Law
An object experiencing an external unbalanced net force will accelerate. The size of the acceleration will depend (inverse
dependance) on the size of the inertial mass of the object.
# = 𝒎𝒂
#
!𝑭
𝒎 = 𝒊𝒏𝒆𝒓𝒕𝒊𝒂𝒍 𝒎𝒂𝒔𝒔
" = 𝒂𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏
𝒂
𝒎
𝑼𝒏𝒊𝒕 𝒐𝒇 𝒇𝒐𝒓𝒄𝒆 𝒊𝒔 𝒄𝒂𝒍𝒍 𝑵𝒆𝒘𝒕𝒐𝒏(𝑵) = 𝒌𝒈 𝟐
𝒔
You chose this option if either you know the object is accelerating, or if you don’t know if the forces are balanced. Keep in mind, there are
different kinds of accelerations.
1)
Accelerations in which the speed of an object is changing.
𝑎 = Δ𝑣&𝑡 (AP 1) or 𝑎 = 𝑑𝑣&𝑑𝑡 (AP C).
2)
Centripetal accelerations (accelerations in which the object is traveling in a curved path while the speed doesn’t change
"
𝑎! = 𝑣 &𝑟 where r is the radius of curvature of the path the object is traveling upon.
Newton’s Third Law
For EVERY force there is an equal but opposite reactive force. These forces act on separate objects that are connected
by this force. An object can’t touch another object without itself being touched. ALL forces come in action reaction pairs.
" 𝟏𝟐 = 𝑭
" 𝟐𝟏
𝑭
Objects are connected by force. You push on a chair, it pushes on you. How effective a force is at causing a change depends on the object. For
example, there is a gravitational force pulling down on you from the Earth. There is an equal but opposite force pulling up on the Earth from you.
The gravitational force on you is very effective at pulling you down as you have very little inertia compared to the Earth. The gravitational force
pulling up on the Earth from you is very ineffective at accelerating the Earth. Use Newton’s 1st and 2nd law to determine how effective a force is at
accelerating or changing the motion of the object.
Shelton
Instructional Support Notes
AP Physics 1 and C: Mechanics
Unit 2: Force and Translational Dynamics
Framework for Solving Force Problems
AP Physics 1 and AP Physics C: Mechanics
Step 1: Decide if this is a 1st Law or 2nd Law Problem
#=𝟎
1st Law Problems: ∑ 𝑭
Net force is zero
All forces are balanced
Acceleration is Zero
Object is at rest or has a constant velocity (traveling at the same speed and in the same direction)
# = 𝒎𝒂
#
2nd Law Problems: ∑ 𝑭
Net force is NOT zero
All forces are NOT balanced
Acceleration is NOT zero
Object has either a changing speed, changing direction or both
Step 2: Draw a Free Body Diagram (FBD)
A. Reduce the shape and size of each object to a single dot representing the center of mass of the object.
B. Add each force acting on the object
Each force acting on the object is represented as a single arrow beginning on the dot and extending in away in the direction of the force. Go
down this list and ask yourself if any of these forces apply to your problem. For most problems, you will only have a handful of forces on
each object. The most common forces will be gravity, tension, normal, and friction.
1.
Fundamental forces first: (we only have one of these forces but as a rule there are many)
o
o
o
o
o
2.
Gravitational force (FG, W, mg)(only one that matters in this class)
Electrostatic force (only matters in E&M)
Elecromagnetic force (only matters in E&M)
Weak Nuclear force (whoa, don’t even think of if)
Strong Nuclear force (no way)
Contact Forces: only occur through contact so only consider them if they meet the criteria described.
o
o
o
o
o
Tension Force (T, FT) – pulling forces that are caused by strings, cables, or some connection (your arm could cause tension on a
chair if you pulled it across a room)
§
Spring or Hook’s Law Force– special case of a tension force caused by a spring. A spring will stretch as the force it
applies increases. A Hook’s Law spring will stretch proportional to the size of the force:
Normal Force (N, FN) – pushing forces that occur if the object is in contact with ANY surface. These forces are perpendicular to
the surface in contact (technically the word NORMAL means perpendicular).
§
Spring or Hook’s Law Force– special case of a normal force caused by a spring. A spring will compress (get smaller)
as the force it applies increases. A Hook’s Law spring will compress proportional to the size of the force:
Frictional Force (f, Ff) – A force that will be in the direction that opposes the motion of the object with respect to the surface. It
is proportional to the “stickiness” of the surface. The object MUST be in contact with a surface to experience friction, so the
object will always be experiencing a normal force as well.
§
Static Friction (fs)– Also called starting friction, it is the amount of frictional force acting to PREVENT an object from
sliding. This ONLY occurs if the object is at rest. This force will increase to keep in object from moving and must be
broken for an object to actual begin to slide.
§
Kinetic Friction (fk)– Also called sliding friction, it occurs between two surfaces that are sliding with respect to each
other.
Air Resistance or Drag (FD) – A force that opposes an object that moves through a fluid (air or liquid). It can be proportional to
the velocity of the object or proportional to the square of the velocity of the object. Which means the faster you go the bigger this
force must be. It is in the opposite direction of the velocity of the object. So if the object is not moving, there is no drag.
(conceptually in AP 1 and mathematically in Mechanics)
Buoyant Force or Archimedes Force (FB) – This force buoys’ an object to the surface of a fluid. It occurs because of gravity and
will always be in the opposite direction of gravity towards the surface of the liquid. It is proportional the weight of the fluid
displaced. (AP 1 only)
C. Apply a coordinate system to be used to solve the problem.
Choose the direction to be represented as positive. This is a standard X,Y cartesian coordinate plane and remember, it is just two number
lines that are perpendicular to each other. The origin goes on the ‘dot’ of the free body diagram (FBD).
Shelton
Instructional Support Notes
AP Physics 1 and C: Mechanics
Unit 2: Force and Translational Dynamics
Framework for Solving Force Problems
AP Physics 1 and AP Physics C: Mechanics
Priorities of your coordinate system:
1. Align the positive x or y direction with the direction of the acceleration so the acceleration is aligned with only one of the
coordinate systems.
If that doesn’t work or if the object isn’t accelerating, then go with the second priority.
2. Align the coordinate system so that it is aligned with the greatest number of forces.
Off Axis Forces
Any force that is not aligned with one of the coordinate directions MUST be broken up in its component forces aligned with the x and y
direction. So apply the appropriate trigonometry to get your components.
Step 3: Apply Newton’s Law
Generate a force relationship for each coordinate direction (one for the x direction and one for the y direction). Remember that Newton’s
Laws are instructions not equations. So look at the forces in the X direction and then look at the forces in the Y direction. In the end you
will produce ∑ 𝐹# and ∑ 𝐹$ and set them to either 0 or ma.
Consider possible substitutions:
& & %
Gravity: 𝑊 = 𝑚𝑔 or 𝐹% = ! " "
'
Friction: static friction: 𝑓( ≤ 𝜇( 𝑁 or kinetic friction: 𝑓) = 𝜇) 𝑁
Hook’s Law: 𝐹2( = −𝑘 ∙ Δ𝑥̅
Drag: 𝐹2* = −𝑐𝑣
Add known or given values to your relationships.
Step 4: Solving the problem
This process just generates relationships. It doesn’t solve the problem. That is why you are here. To look at the result of applying the
process. You must assess and find a pathway to reduce your number of equations and solve for your unknowns. Remember you are
generating a system of relationships. For the most part these relationships should be able to answer the question in the problem.
Common Question Types:
o
o
o
o
Find an individual force.
o Examples:
§
How much tension is in the rope?
§
How hard do you have to push?
§
What was the size of the frictional force?
o This answer will sometimes ask for the direction of the force, but will always be in Newtons.
Find the acceleration.
o These must be a second law problem
o This answer will be m/s/s.
o Could be hidden inside of a motion equation problem. Remember the problem may ask for a velocity or displacement,
but you will likely use the force problem to get the acceleration first.
Find an ancillary piece of information
o Examples:
§
Find the coefficient of friction
•
The coefficient of friction is part of the friction equation
§
Find the spring constant
•
The spring constant is part of Hook’s Law
Find a conditional response
o Example
§
At what angle will pushing on an object get it to slide across the floor?
§
What coefficient of friction will keep the block from moving?
§
How far is the spring stretched before the system begins moving?
o Conditional problems generally have a force that can change size based on some condition
§
Friction depends on the coefficient and the normal force,
§
Hooks law depends on the type of spring and how far it is compressed or stretched
Shelton
Instructional Support Notes
AP Physics 1 and C: Mechanics
Unit 2: Force and Translational Dynamics
Framework for Solving Force Problems
AP Physics 1 and AP Physics C: Mechanics
Shelton
Examples
AP Physics 1 and C: Mechanics
Unit 2: Force and Translational Dynamics
Framework for Solving Force Problems
AP Physics 1 and AP Physics C: Mechanics
Shelton
Examples
AP Physics 1 and C: Mechanics
Unit 2: Force and Translational Dynamics
Framework for Solving Force Problems
AP Physics 1 and AP Physics C: Mechanics
Shelton
Examples
AP Physics 1 and C: Mechanics
Unit 2: Force and Translational Dynamics