1. Forces & vectors
Dynamics
lesson 2

2. …vectors? - + It is a segment represented with an arrow.
origin
tip
Properties:
Magnitude: length of the vector
Magnitude: length of the vector
Direction: set of parallel lines where the vector is located
Direction: set of parallel lines where the vector is located
Sense: Any of the two possible (+) or (-)
Sense: Any of the two possible (+) or (-)

3. Force is a vector not always!! Are the effects going to be the same? F
Forces produce changes in motion
Forces produce changes in motion
Forces produce changes in motion
Forces produce changes in motion
not always!!
not only is magnitude important but also the direction and the sense of the force
not only is magnitude important but also the direction and the sense of the force
not only is magnitude important but also the direction and the sense of the force
not only is magnitude important but also the direction and the sense of the force
Are the effects going to be the same? F F F

4. Obviously FR will accomplish Newton’s 2nd law
Force addition
FR = F1 + F2
FR = F1 + F2
FR = F1 + F2 FR
Graphical addition F2 F1
1 – Move F2 to the tip of F1
2 – Join the origin of F1 and the tip of F2
This new vector is FR
simulation
Obviously FR will accomplish Newton’s 2nd law
FR = m·a

5. We will use Pythagoras's theorem
Force decomposition
also known as
Resolution of a force into its components
Resolution of a force into its components
Relabeling the vectors:
According to previous slide:
FR = F1 + F2
F = Fx + Fy
FR = F1 + F2 F FR Fy F2
Let’s calculate the magnitude of FR
We will use Pythagoras's theorem F1 Fx
Let’s practise!!
simulation

6. Fg or P Kinds of forces I Weight F = m · a a = g = -9’8 m/s2 P = m · g
Force due to the attraction of the Earth.
Force due to the attraction of the Earth.
Weight
According to Newton’s 2nd law:
F = m · a
In this case acceleration is gravity
In this case acceleration is gravity
Fg or P
a = g = -9’8 m/s2
So weight is represented by:
P = m · g

7. Normal is found balancing forces
Kinds of forces II
Force due to the presence of surfaces.
Force due to the presence of surfaces.
Normal N P N
Obviously, force of gravity is acting too...
In this case:
N = P
Normal is found balancing forces
not always!!!

8. Tension is found balancing forces
Kinds of forces III
Force due to ropes, strings, wires...
Tension T P T
Obviously, force of gravity is acting too...
In this case:
T = P
Tension is found balancing forces
not always!!!

9. Fm Kinds of forces IV Friction Fm = -m · N m
Force due to the contact of two surfaces.
Force due to the contact of two surfaces.
Friction N Fm P Fm
Sense of friction is opposite to movement
Fm = -m · N m
Friction coefficient
It depends on the two surfaces
It depends on the two surfaces

10. Situations were forces need to be decomposed
Force diagrams
N + P = 0
Fm = m · a
Ty + P = 0
Tx = m · a
Pt + Fm = m · a
N + Ph = 0
FR = m · a
P = m · a
N + P = 0
T + P = 0 N N Fm T P P P P Fm N
Situations were forces need to be decomposed T Ty Pt Ph P Tx
tangential direction
normal direction P