Leyes del movimiento de Newton

Transcripción

1 Leyes del movimiento de Newton Ejemplos de la ubicación de las fuerzas que intervienen en un sistema aislado. Ejemplos de problemas a resolver con las Leyes de Newton. Tomados de los textos de Física Universitaria 1 de Serway-Jewett, Bauer-Westfall, Tipler-Mosca. September 27, 2012 Physics for Scientists&Engineers 1 1

2 Sir Isaac Newton Born Jan 4, 1643, Woolsthorpe, Lincolnshire, England June 5, 1661: Entered Trinity College, Cambridge April 1665: Bachelor s Degree Summer 1665 to 1667: University is closed due to plague; Newton returns home and makes his major advances in math, physics, astronomy 1666: Universal law of gravitaton 1669: Newton is appointed Lucasian Chair at Cambridge 1670: Particle theory of light 1671: Publication of Calculus (later independently invented by German Leibniz) 1687: Publication of Principia (Newton s 3 Laws of Motion) 1689: Election to Parliament 1696: Warden of the Royal Mint 1699: Master of the Royal Mint (becomes very rich!) 1703: Elected President of Royal Society 1705: Knighted by Queen Anne March 31, 1727: Died in London September 27, 2012 Physics for Scientists&Engineers 1 2

3 Sir Isaac Newton s burial site in Westminster Abbey September 27, 2012 Physics for Scientists&Engineers 1 3

4 Fuerzas de contacto y fuerzas de acción a distancia (con intervención de un campo) September 27, 2012 Physics for Scientists&Engineers 1 4

5 September 27, 2012 Physics for Scientists&Engineers 1 5

6 Computadora Notebook Hand exerts a force on computer: N (normal force) This force points in opposite direction to weight, and has same magnitude N F g September 27, 2012 Physics for Scientists&Engineers 1 6

7 Otro ejemplos de fuerzas September 27, 2012 Physics for Scientists&Engineers 1 7

8 Cuerdas y poleas The force is transmitted exactly in the direction of the rope Force inside the rope is called tension September 27, 2012 Physics for Scientists&Engineers 1 8

9 Cuerdas y poleas Tension is the same everywhere inside the rope Ropes can be redirected via pulleys => direction of force changes, but not absolute magnitude September 27, 2012 Physics for Scientists&Engineers 1 9

10 DOS POLEAS Mass m hung from a system of two pulleys September 27, 2012 Physics for Scientists&Engineers 1 10

11 Ejemplo de anillos olímpicos Gymnast of mass 55 kg hangs from still rings. Question 1: What is the tension in each rope? September 27, 2012 Physics for Scientists&Engineers 1 11

12 Ejemplo de anillos olímpicos Answer: no forces in x-direction; in y-direction: F y,i T 1 T 2 mg 0 i Both ropes support the gymnast equally T 1 T 2 T T T mg 0 T 1 2 mg 1 2 (55 kg) (9.81 m/s2 ) 270 N September 27, 2012 Physics for Scientists&Engineers 1 12

13 Plano inclinado Typical situation: an object slides down a plane that is at some angle relative to the horizontal Example: Snowboarding September 27, 2012 Physics for Scientists&Engineers 1 13

14 Plano inclinado N F g September 27, 2012 Physics for Scientists&Engineers 1 14

15 Plano inclinado Step 2: Pick a convenient coordinate system For inclined-plane problems, it is almost always advisable to select the x- axis along the plane (positive to the right, y-axis perpendicular to it, of course) Note: normal force has only a component in y direction Decompose weight force into components N mgsin y mgcos F g x September 27, 2012 Physics for Scientists&Engineers 1 15

16 Otro ejemplo de movimiento y fuerzas en plano inclinado September 27, 2012 Physics for Scientists&Engineers 1 16

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18 Ejemplo para clase Descarga de un camión: Se desea descargar una caja enorme y frágil desde un camión usando una rampa. Si la velocidad vertical con la que la caja llega al final de la rampa es superior a 2.5 m/s ( la velocidad que adquiere un objeto si se cae desde una altura de 30.5 cm), se daña. Cuál es el mayor ángulo posible al que se debe instalar la rampa para tener una descarga segura? La rampa debe superar 1 m de altura, inclinada un ángulo y está formada por rodillos que no ejercen rozamiento. September 27, 2012 Physics for Scientists&Engineers 1 18

19 Ejemplo de fuerzas de tensión September 27, 2012 Physics for Scientists&Engineers 1 19

20 Tarea para practicar. No se entrega September 27, 2012 Physics for Scientists&Engineers 1 20