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Dynamics: Intro & Application of Newton’s Laws
Drawing Free-Body-DiagramsAP Physics Development
Committee May 2010 – New Wording for free-body or force diagrams. (p. 149 C&E)Students will be directed to "draw and label the forces (not components) that act on the [object]," where [object] is replaced by a reference specific to the question, such as "the car when it reaches the top of the hill." Any components that are included in the diagram will be scored in the same way as incorrect or extraneous forces.
Drawing Free-Body-DiagramsIn addition, in any subsequent part asking for a solution that would typically make use of the diagram, the following will be included. "If you need to draw anything other than what you have shown in part [x] to assist in your solution, use the space below. Do NOT add anything to the figure in part [x]." This will give students the opportunity to construct a working diagram showing any components that are appropriate to the solution of the problem. This second diagram will not be graded.
Drawing Free-Body-DiagramsBinder pp. 19-21
Force: interaction between an agent and an object causing a push or pull
Force = Interaction
Two kinds of forces 1. Contact 2. “Non-Contact” (long-range
field forces due to gravitational, magnetic, and/or electric fields)
Force TypesContact
Supportive (normal or ⊥) NTension (rope/chain) T
Friction or Drag (always oppose motion)
f
Other push or pull PNon-Contact
Gravitational G
System Schema
block
table
earth
Identify the interactions
System Schema
block
table
earth
label the interaction types
NG
G
System Schema
block
table
earth
Dot around the system of interest
NG
G
System Schema
block
table
earth
You are only interested in the forces that cross the dotted line!
NG
G
Type of force
Agent that produces the force.“Dealer”
Object the force acts on.
“Feeler”
Agent/Object Notation
If the agent can't be identified, the force doesn't exist!
FN T/B
FG E/B
Constant Velocity
block
table
earth
NG
G
Note: the velocity vector does NOT touch the dot.
When the object is moving, include a velocity vector off to the side
FN T/B
FG E/B
Constant Velocity
v
Ff T/B
v
FG E/B
FN T/B
Changing velocity
block
table
earth
NG
G
f
Ff T/B v
FG E/B
FN T/B
Changing velocity
a
Note: the acceleration vector does NOT touch the dot.
v
FG E/B
FN R/B
Non Perpendicular Forces
block
ramp
earth
NG
G
Object slides without friction
Ff Ramp ll/B = f FN Ramp ⊥/B = FN
FG E/B= Wt
Another form of A/O notationComponents should not appear on the FBD!!
Non Perpendicular Forces
FT Rope1/B = T1
FG E/B= Wt
FT Rope2/B = T2
Unambiguous Force Labeling
FG E/B = mg
FT R/B= T
θ Ff Tll/B = f
FN T⊥/B = FN
v
Forces – Relative lengths
Ff A/B= D
FG E/B= mg
v
FG E/B= mg
v
Ambiguity in HW is OK
OR
Isaac Newton (1642-1727)
NEWTON'S LAWSFIRST LAWObject at rest or moving with constant velocity.
ΣF = 0 (Equilibrium)Vectors should be written in component form:
ΣFx = 0ΣFy = 0
2005 B2. A simple pendulum consists of a bob of mass 1.8 kg attached to a string of length 2.3 m. The pendulum is held at an angle of 30° from the vertical by a light horizontal string attached to a wall, as shown. a. Draw a free‑body
diagram labeling the forces on the bob in the position shown.
2005B2
FT s2/B=T2
FT s1/B = T1
FG E/B= mg
b. Calculate the tension in the horizontal string. ΣFH = T2 – T1 cos 60º =
0ΣFV = T1 sin 60º - mg = 0
T2 = 10.18 N
T2
T1
mg
60°
c. The horizontal string is now cut close to the bob, and the pendulum swings down. Calculate the speed of the bob at its lowest position.L
hh = L - Lcosθ
= 2.5 m/s
The End (for now)