1 / 27

Magnitudes vectoriales

Magnitudes vectoriales. force: action of one body on another; characterized by its point of application , magnitude , line of action , and sense. Experimental evidence shows that the combined effect of two forces may be represented by a single resultant force.

joannwashington
Télécharger la présentation

Magnitudes vectoriales

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Magnitudes vectoriales

  2. force: action of one body on another; characterized by its point of application, magnitude, line of action, and sense. • Experimental evidence shows that the combined effect of two forces may be represented by a single resultant force. • The resultant is equivalent to the diagonal of a parallelogram which contains the two forces in adjacent legs.

  3. Trapezoid rule for vector addition • Triangle rule for vector addition • Law of cosines, C B C • Law of sines, B • Vector addition is commutative, • Vector subtraction Addition of Vectors

  4. Addition of three or more vectors through repeated application of the triangle rule • The polygon rule for the addition of three or more vectors. • Vector addition is associative, • Multiplication of a vector by a scalar Addition of Vectors

  5. Concurrent forces: set of forces which all pass through the same point. A set of concurrent forces applied to a particle may be replaced by a single resultant force which is the vector sum of the applied forces. • Vector force components: two or more force vectors which, together, have the same effect as a single force vector. Resultant of Several Concurrent Forces

  6. Sample Problem 2.1 • SOLUTION: • Graphical solution - construct a parallelogram with sides in the same direction as P and Q and lengths in proportion. Graphically evaluate the resultant which is equivalent in direction and proportional in magnitude to the the diagonal. The two forces act on a bolt at A. Determine their resultant. • Trigonometric solution - use the triangle rule for vector addition in conjunction with the law of cosines and law of sines to find the resultant.

  7. Graphical solution - A parallelogram with sides equal to P and Q is drawn to scale. The magnitude and direction of the resultant or of the diagonal to the parallelogram are measured, • Graphical solution - A triangle is drawn with P and Q head-to-tail and to scale. The magnitude and direction of the resultant or of the third side of the triangle are measured, Sample Problem 2.1

  8. Sample Problem 2.1 • Trigonometric solution - Apply the triangle rule.From the Law of Cosines, From the Law of Sines,

  9. May resolve a force vector into perpendicular components so that the resulting parallelogram is a rectangle. are referred to as rectangular vector components and • Define perpendicular unit vectors which are parallel to the x and y axes. • Vector components may be expressed as products of the unit vectors with the scalar magnitudes of the vector components.Fx and Fyare referred to as the scalar components of Rectangular Components of a Force: Unit Vectors

  10. Wish to find the resultant of 3 or more concurrent forces, • Resolve each force into rectangular components • The scalar components of the resultant are equal to the sum of the corresponding scalar components of the given forces. • To find the resultant magnitude and direction, Addition of Forces by Summing Components

  11. Sample Problem 2.3 • SOLUTION: • Resolve each force into rectangular components. • Determine the components of the resultant by adding the corresponding force components. • Calculate the magnitude and direction of the resultant. Four forces act on bolt A as shown. Determine the resultant of the force on the bolt.

  12. SOLUTION: • Resolve each force into rectangular components. • Determine the components of the resultant by adding the corresponding force components. • Calculate the magnitude and direction. Sample Problem 2.3

  13. The vector is contained in the plane OBAC. • Resolve into horizontal and vertical components. • Resolve into rectangular components Rectangular Components in Space

  14. Rectangular Components in Space

  15. With the angles between and the axes, • is a unit vector along the line of action ofand are the direction cosines for Rectangular Components in Space

  16. Vectores unitarios • El valor de la tension en el cable AB es de 2500 N. Determine: • Las componentes Fx, Fy, Fz de la fuerza que actúa sobre el perno A • ,b) the angles qx, qy, qzque definen la dirección de la fuerza • Planteamiento: • Utilizando las posiciones relativas, hallar el vector unitario que va de A hacia BUsamos el vector unitario para hallar las componentes de la Fuerza que actúa en A • Note que las componentes del vector unitario son los cosenos directores del vector • Se calculan los correspondientes ángulos

  17. Determine the components of the force. • Solución • El vector unitario de A hacia B es

  18. Y 10 m 8 m F 200Kg X 12 m Z

  19. En la figura la fuerza F se encuentra en el plano definido por las líneas LA y LB que se intersecan. Su magnitud es de 400 lb. Supongamos que F se quiere separar en componentes paralelas a LA y a LB. Determine las magnitudes de las componentes vectoriales:gráficamenteAnalíticamente

  20. B A 30° C En la fig. los cables AB y AC ayudan a soportar el techo voladizo de un estadio deportivo. Las magnitudes de las fuerzas FAB y FAC son 100KN y 60 KN respectivamente, encuentre la fuerza neta ejercida sobre la pila por los cables

  21. F 60° LB 80°¬|°° 0¬| LA F 60° LB 80°¬|°° 0¬| LA

More Related