Forces & vectors Dynamics lesson 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 (-)

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

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

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

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

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!!!

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!!!

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

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