Kinetics of Particles Newton’s Laws •Newton´s First Law or the Law of the Inertia •Newton´s Second Law: Force, mass and acceleration Momentum or Linear Momentum Principles of Conservation •Newton´s Third Law •Forces in Nature. Free body Diagram •Equations of Motion

Newton´s Laws. Dealing with Forces FIRST LAW: If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion) SECOND LAW: If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitud of the resultant and in the direction of the resultant force. THIRD LAW: The forces of action and reaction between bodies in contact have the same magnitude, same line of action and opposite sense

Concepts involved: Space, Time, Mass and Force Space and Time unable describe the motion Mass is a property of bodies that is defined by the effect on the change of translational motion when the forces acting on bodies, or by the atraction by the earth. A force represents the action of one body on another. It can be exerted by actual contact or at a distance (gravitational, electrical, magnetical,… forces)

Force, Mass, and Newton’s Second Law

r r F = m a ∑

To apply this equation, the acceleration must be determined with respect to a newtonian frame of reference (inertial or non accelerated)

r r r d v d m v ( ) r ∑ F = m a = m dt = dt r d pr ∑ F = dt

Momentum or Linear momentum

r r p = mv

The resultant of the forces acting on the particle is equal to the rate of the change of the linear momentum of the particle. In this forrm the second law of motion was originally stated by Newton.

Principle of Conservation of Linear Momentum: If the resultant force acting on a particle is zero, the linear momentum of a particle remains constant, in both magnitude and direction.

Sistem of Units, International System of Units SI, F, force, expressed in Newtons, [N]; m, mass, expressed in kilograms,[kg]: a, acceleration, expressed in meter per squared second, [m/s2] or [m s-2] 1 N = 1 kg · m/s2

Problem Solving: Free-Body Diagrams

Forces in Nature A force represents the action of one body on another. It can be exerted by actual contact or at a distance (gravitational, electromagnetic,… forces) The Fundamental Forces: 1.- The gravitational force, the force of mutual atraction between material objects; 2.- The electromagnetic force, the force between electric charges, 3.- The strong nuclear force; 4.- The weak nuclear force Action a distance: The concept of field Contact Forces The Force Due to the Gravity: The weight W of a body, or force of gravity is the force exerted on the body by the atraction of earth.

r r w=mg

g = 9,806 ≅ 9,81 m s −2

The weight, like any other force must be expressed in Newtons. The weight is applied on the center of mass, in the case of a extent body. Is there gravitational force acting on the astronaut at the International Space Station?. It is situated around a height of 400 km above of Earth surface.

Forces in Nature

Dealing with Forces. Free-Body Diagram

Free Body Diagram: A diagram that shows all external forces acting on a body At distant forces: Gravitational, Electromagnetic,..the concept of field Contact Forces: Connections and supports, Friction, Cables, Spring, …..

Forces in Nature

Dealing with Forces. Free-Body Diagram Reactions at Supports and Connections for a Two-Dimensional Structure Reactions Equivalent to a Force with Known Line of Action. Each of these supports and connections can prevent motion in one direction only

In this case “short” means without weight

Each of the reactions here considered involves one unknown –the magnitude-. Usually direction is known by the geometry and need to be indicated clearly in the free-body diagram

Forces in Nature

Dealing with Forces. Free-Body Diagram Reactions at Supports and Connections for a Two-Dimensional Structure • This type can prevent translational but no rotating around the connection • Reactions equivalent to a force of unknown direction and magnitude. • They constraint completely the motion • Reactions equivalent to a force and a couple, involving three unknowns, usually the two components of the forces and the magnitude of the couple

Exercises

Free-Body Diagram Frictionless Surface

Rough Surface in Contact

Friction Dry friction happens between rigid bodies which are in contact along non lubricated surfaces; Fluid friction develops between layers of fluid moving at different velocities.

FRICTION Static friction

Kinetic friction

When an ideal, rigid wheel rolls at constant speed along an ideal, rigid horizontal road without slipping no frictional force is acting in the contact point. However real wheel and real road deform and interact between them; so, the road exerts a force of rolling friction that opposes the motion.

Friction explained Friction is a force between two surfaces in contact; Friction always opposes motion, or the tendency to motion, of each surface relative to the other surface The friction force is not dependent of the area of the contacting bodies, but only the effective contact area between surfaces Friction is a complex , incompletely understood phenomenon that arises from the attraction of molecules between two surface that are in close contact.

Exercises The block of mass m2 has been adjusted so that block of mass m1 is on the verge of sliding. (a) If m1 = 7 kg and m2 = 5 kg, what is the coefficient of static friction between the table an the block. (b) With a slight nudge , the system starts the motion. Find their acceleration. Coefficient of kinetic friction, 0,54

A curve of radius 30 m is banked at an angle for which a car can round the curve a 40 km/h even the road is covered with ice so that friction force is negligible. Find this angle.

Drag Forces Fluid friction Drag skin, Drag form The magnitude of drag force, Fd, for an object on free n fall is

Fd = bv

where: v : speed of the object relative to the air b is a constant, depending of the object form; n depends of the object form and of the speed, v, a typical value is 2

Problems

Una pequeña cuenta de 100 g de masa desliza sin fricción sobre un alambre semicircular con un radio de 10 cm que rota alrededor de un eje vertical a un ritmo de de 2 revoluciones por segundo. Encontrar el valor del ángulo indicado en la figura para el cual la cuenta permanecerá en equilibrio relativo al alambre.

A block of mass m1 is attached to a cord of lenghtz L1, which is fixed at one end. The block moves I a horizontal circle on a frictionless tabletop. A secod block of mass m2 is attached to the first by a cord of lenghtz L2 and also moves in a circle on the same frictionless table top, as showown in the figure. If the period of the motion is T, find the tension in each cord.

A small bead with a mass of 100 g slides without friction along a semicircular wire with a radius of 10 cm that rotates about a vertical axis at a rate of 2.0 revolutions per second . Find the value of the angle θ for which the bead remain stationary relative to the rotating wire.