dynamics: intro & application of newton’s laws

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)