Mecânica Aplicada REVIEW PROBLEMS Cap.121 - Cinética das...

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Departamento de Engenharia Mecânica Área Científica de Mecânica dos Meios Sólidos RMM – 2015/16 Mecânica Aplicada Cap.12 1 - Cinética das partículas Problema 12.9 Um pacote de 40 está em repouso sobre um plano inclinado quando uma força é aplicada sobre ele. Determine a intensidade de se são necessários 4 para o pacote percorrer 10 subindo no plano inclinado. Os coeficientes de atrito estático e dinâmico entre o pacote e o plano inclinado são 0,30 e 0,25, respectivamente. Problema 12.22 Para transportar uma série de pacotes de telhas para um telhado, um empreiteiro usa um elevador movido a motor que consiste de uma plataforma horizontal que se desloca sobre trilhos presos aos lados da uma escada. O elevador parte do repouso e se move inicialmente com uma aceleração ! , tal como mostra a figura. O elevador então desacelera a uma taxa constante ! e chega ao repouso em , perto do topo da escada. Sabendo que o coeficiente de atrito estático entre o pacote de telhas e a plataforma horizontal é de 0,30, determine a maior aceleração possível ! e a maior desaceleração possível ! para que o pacote não escorregue sobre a plataforma. Problema 12.125 As massas dos blocos A, B e C são ! = 4 , ! = 10 e ! = 2 . Sabendo que = 0 e desprezando as massas das roldanas e o efeito do atrito, determine: (a) a aceleração de cada bloco; (b) a tração na corda. Problema 12.128 Uma pista de montanha-russa mostrada na figura está contida num plano vertical. A parte da pista entre e é recta e horizontal, enquanto que as partes à esquerda de e à direita de têm raios de curvatura como indicado. O carro está se movendo a uma velocidade escalar de 72 /quando os freios são repentinamente acionados, fazendo com que as rodas do carro deslizem sobre a pista ( ! = 0,25). Determine a desaceleração inicial do carro se os freios são acionados quando ele: (a) está quase a chegar a , (b) está se movendo entre e , (c) acabou de passar por . 1 Os problemas apresentados referem-se ao livro “Mecânica Vetorial para Engenheiros – Dinâmica, Ferdinand P. Beer, E. Russell Johnston Jr., William E. Clausen, 7ªEd McGraw-Hill” 30° 20° P A B C 4.4 m 65° 0.8 m a 1 D A B = 45 m r = 30 m r

Transcript of Mecânica Aplicada REVIEW PROBLEMS Cap.121 - Cinética das...

  • DepartamentodeEngenhariaMecânicaÁreaCientíficadeMecânicadosMeiosSólidos

    RMM–2015/16

    MecânicaAplicada

    Cap.121-CinéticadaspartículasProblema12.9

    Um pacote de40 𝑘𝑔 está em repouso sobre um plano inclinadoquandoumaforça𝑷éaplicadasobreele.Determineaintensidadede𝑷se são necessários4 𝑠 para o pacote percorrer10 𝑚 subindo noplano inclinado.Oscoeficientesdeatritoestáticoedinâmicoentreopacoteeoplanoinclinadosão0,30e0,25,respectivamente.

    Problema12.22

    Para transportar uma série de pacotes de telhas𝐴para umtelhado,umempreiteirousaumelevadormovidoamotorqueconsistedeumaplataformahorizontal𝐵𝐶quesedeslocasobretrilhos presos aos lados da uma escada. O elevador parte dorepouso e se move inicialmente com uma aceleração𝒂!, talcomomostraafigura.Oelevadorentãodesaceleraaumataxaconstante𝒂!echegaaorepousoem𝐷,pertodotopodaescada.Sabendoqueocoeficientedeatritoestáticoentreopacotedetelhas e a plataformahorizontal é de0,30, determine amaioraceleraçãopossível𝒂!eamaiordesaceleraçãopossível𝒂!paraqueopacotenãoescorreguesobreaplataforma.

    Problema12.125

    As massas dos blocos A, B e C são𝑚! = 4 𝑘𝑔 ,𝑚! = 10 𝑘𝑔 e𝑚! = 2 𝑘𝑔 . Sabendo que𝑃 = 0 e desprezando as massas dasroldanaseoefeitodoatrito,determine:

    (a) aaceleraçãodecadabloco;(b) atraçãonacorda.

    Problema12.128

    Uma pista de montanha-russa mostrada na figura estácontida numplano vertical. A parte da pista entre𝐴e𝐵érectaehorizontal,enquantoqueaspartesàesquerdade𝐴e à direita de𝐵têm raios de curvatura como indicado. Ocarro está se movendo a uma velocidade escalar de72 𝑘𝑚/ℎquando os freios são repentinamente acionados,fazendocomqueasrodasdocarrodeslizemsobreapista(𝜇! = 0,25).Determineadesaceleração inicialdocarroseosfreiossãoacionadosquandoele:

    (a) estáquaseachegara𝐴,(b) estásemovendoentre𝐴e𝐵,(c) acaboudepassarpor𝐵.

    1Osproblemasapresentadosreferem-seaolivro“MecânicaVetorialparaEngenheiros–Dinâmica,FerdinandP.Beer,E.RussellJohnstonJr.,WilliamE.Clausen,7ªEdMcGraw-Hill”

    707Problems 12.6 Determine the maximum theoretical speed that an automobile starting from rest can reach after traveling 400 m. Assume that the coefficient of static friction is 0.80 between the tires and the pavement and that (a) the automobile has front-wheel drive and the front wheels support 62 percent of the automobile’s weight, (b) the automobile has rear-wheel drive and the rear wheels sup-port 43 percent of the automobile’s weight.

    12.7 In anticipation of a long 7° upgrade, a bus driver accelerates at a constant rate of 3 ft/s2 while still on a level section of the highway. Knowing that the speed of the bus is 60 mi/h as it begins to climb the grade and that the driver does not change the setting of his throttle or shift gears, determine the distance traveled by the bus up the grade when its speed has decreased to 50 mi/h.

    12.8 If an automobile’s braking distance from 60 mph is 150 ft on level pavement, determine the automobile’s braking distance from 60 mph when it is (a) going up a 5° incline, (b) going down a 3-percent incline. Assume the braking force is independent of grade.

    12.9 A 20-kg package is at rest on an incline when a force P is applied to it. Determine the magnitude of P if 10 s is required for the package to travel 5 m up the incline. The static and kinetic coef-ficients of friction between the package and the incline are both equal to 0.3.

    12.10 The acceleration of a package sliding at point A is 3 m/s2. Assuming that the coefficient of kinetic friction is the same for each section, determine the acceleration of the package at point B.

    30°

    20°

    P

    Fig. P12.9

    15°

    A

    B

    30°

    Fig. P12.10

    A

    30 kg

    25 kgB

    Fig. P12.11 and P12.12

    12.11 The two blocks shown are originally at rest. Neglecting the masses of the pulleys and the effect of friction in the pulleys and between block A and the horizontal surface, determine (a) the acceleration of each block, (b) the tension in the cable.

    12.12 The two blocks shown are originally at rest. Neglecting the masses of the pulleys and the effect of friction in the pulleys and assuming that the coefficients of friction between block A and the horizontal surface are ms 5 0.25 and mk 5 0.20, determine (a) the accelera-tion of each block, (b) the tension in the cable.

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    710 Kinetics of Particles: Newton’s Second Law 12.22 To transport a series of bundles of shingles A to a roof, a contractor uses a motor-driven lift consisting of a horizontal platform BC which rides on rails attached to the sides of a ladder. The lift starts from rest and initially moves with a constant acceleration a1 as shown. The lift then decelerates at a constant rate a2 and comes to rest at D, near the top of the ladder. Knowing that the coeffi-cient of static friction between a bundle of shingles and the hori-zontal platform is 0.30, determine the largest allowable acceleration a1 and the largest allowable deceleration a2 if the bundle is not to slide on the platform.

    A

    B C

    4.4 m

    65°

    0.8 m

    a1

    D

    Fig. P12.22

    2 m 20°A

    Fig. P12.23

    12.23 To unload a bound stack of plywood from a truck, the driver first tilts the bed of the truck and then accelerates from rest. Knowing that the coefficients of friction between the bottom sheet of plywood and the bed are ms 5 0.40 and mk 5 0.30, determine (a) the smallest acceleration of the truck which will cause the stack of plywood to slide, (b) the acceleration of the truck which causes corner A of the stack to reach the end of the bed in 0.9 s.

    12.24 The propellers of a ship of weight W can produce a propulsive force F0; they produce a force of the same magnitude but of opposite direction when the engines are reversed. Knowing that the ship was proceeding forward at its maximum speed v0 when the engines were put into reverse, determine the distance the ship travels before coming to a stop. Assume that the frictional resistance of the water varies directly with the square of the velocity.

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    REVIEW PROBLEMS

    12.122 A 3000-lb automobile is being driven down a 5° incline at a speed of 50 mi/h when the brakes are applied, causing a total braking force of 1200 lb to be applied to the automobile. Determine the distance traveled by the automobile before it comes to a stop.

    12.123 A 6-kg block B rests as shown on a 10-kg bracket A. The coeffi-cients of friction are ms 5 0.30 and mk 5 0.25 between block Band bracket A, and there is no friction in the pulley or between the bracket and the horizontal surface. (a) Determine the maximum mass of block C if block B is not to slide on bracket A. (b) If the mass of block C is 10% larger than the answer found in a deter-mine the accelerations of A, B, and C.

    12.124 Block A weighs 20 lb, and blocks B and C weigh 10 lb each. Know-ing that the blocks are initially at rest and that B moves through 8 ft in 2 s, determine (a) the magnitude of the force P, (b) the tension in the cord AD. Neglect the masses of the pulleys and axle friction.

    12.125 A 12-lb block B rests as shown on the upper surface of a 30-lb wedge A. Neglecting friction, determine immediately after the system is released from rest (a) the acceleration of A, (b) the accel-eration of B relative to A.

    12.126 The roller-coaster track shown is contained in a vertical plane. The portion of track between A and B is straight and horizontal, while the portions to the left of A and to the right of B have radii of curvature as indicated. A car is traveling at a speed of 72 km/h when the brakes are suddenly applied, causing the wheels of the car to slide on the track (mk 5 0.25). Determine the initial decel-eration of the car if the brakes are applied as the car (a) has almost reached A, (b) is traveling between A and B, (c) has just passed B.

    Fig. P12.123

    C

    BA

    P

    BA C

    D

    Fig. P12.124

    A

    B

    12 lb

    30 lb

    30°

    Fig. P12.125

    A B

    = 45 mr

    = 30 mr

    Fig. P12.126

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