1. Sect. 4-7: Solving Problems with Newton’s Laws; Free Body Diagrams
“It sounds like an implosion!”

2. Newton’s 2nd Law: ∑F = ma VECTOR ADDITION! (Ch. 3)
Forces are VECTORS!!
Newton’s 2nd Law: ∑F = ma
∑F = VECTOR SUM of all forces on mass m
 We need VECTOR addition to add forces in the 2nd Law!
Forces add according to the rules of
VECTOR ADDITION! (Ch. 3)

3. Problem Solving Procedures
Make a sketch. For each object separately, sketch a free-body diagram, showing all the forces acting on that object. Make the magnitudes & directions as accurate as you can. Label each force.
Resolve vectors into components.
Apply Newton’s 2nd Law separately to each object & for each vector component.
Solve for the unknowns.
Note that this often requires algebra, such as solving 2 linear equations in 2 unknowns!

4. Example FR = [(F1)2 + (F2)2](½) = 141 N tanθ = (F2/F1) = 1  θ = 45º
Square Root!
FR = [(F1)2 + (F2)2](½) = 141 N
tanθ = (F2/F1) =  θ = 45º

5. Example 4-9 If the boat moves with acceleration a, ∑F = = FR = ma
FRx = max, FRy = may

6. ∑F = ma, Note: This is the LAST step, NOT the first!
Example 4-9
Illustrates the procedures for Newton’s 2nd Law problems:
STEP 1: Sketch the situation!!
Sketch a “Free Body” diagram for EACH body in problem & draw ALL forces acting on it.
Part of your grade on exam & quiz problems!
STEP 2: Resolve the forces on each body into components
Use a convenient choice of x,y axes
Use the rules for finding vector components from Ch. 3.
STEP 3: Apply N’s 2nd Law to EACH OBJECT SEPARATELY
∑F = ma, Note: This is the LAST step, NOT the first!
We NEED A SEPARATE equation like this for each object!
Resolved into components: ∑Fx = max, ∑Fy = may

7. Conceptual Example 4-10 Moving at constant v, with NO friction,
which free body diagram is correct?