DepartamentodeEngenhariaMecânicaÁreaCientíficadeMecânicadosMeiosSólidos

RMM–2015/16

MecânicaAplicada

Cap.161-CinéticadomovimentoplanoProblema16.5

Sabendo que o coeficiente de atrito estático entre os pneus e aestrada é de0,80para o veículomostradona figura, determine aaceleraçãomáximapossível,numaestradanivelada,considerando:

(a) traçãonasquatrorodas;(b) traçãonasrodastraseiras;(c) traçãonasrodasdianteiras.

Problema16.29

Cada uma das roldanas duplas mostradas na figuratemummomentodeinérciademassade20 𝑘𝑔.𝑚!eestá inicialmente em repouso. O raio externo é de400 𝑚𝑚eointernode200 𝑚𝑚.Determine:

(a) a aceleração angular de cada uma dasroldanas;

(b) a velocidade angular de cada uma dasroldanas depois do ponto𝐴na corda ter-sedeslocado3 𝑚.

Problema16.71

Uma haste delgada uniforme de comprimento𝐿 = 900 𝑚𝑚e massa𝑚 = 1 𝑘𝑔está suspensa livremente a partir de uma articulação em𝐴. Se uma força𝑃deintensidade de3,5 𝑁é aplicada em𝐵horizontalmente para a esquerda(ℎ = 𝐿),determine:

(a) Aaceleraçãoangulardahaste;(b) Ascomponentesdareaçãoem𝐴.

Problema16.114

A haste uniforme𝐴𝐵de massa𝑚 = 6 𝑘𝑔e comprimento2𝐿 = 600 𝑚𝑚estápresaa cursoresdemassadesprezávelquedeslizamsematritoaolongo de hastes fixas. Se a haste𝐴𝐵é libertada a partir do repousoquando𝜃 = 30°,determineimediatamenteapósalibertação:

(a) aceleraçãoangulardahaste;(b) areaçãoem𝐴.

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

PROBLEMS

1040

16.1 A conveyor system is fitted with vertical panels, and a 300-mm rod AB of mass 2.5 kg is lodged between two panels as shown. Knowing that the acceleration of the system is 1.5 m/s2 to the left, determine (a) the force exerted on the rod at C, (b) the reaction at B.

16.2 A conveyor system is fitted with vertical panels, and a 300-mm rod AB of mass 2.5 kg is lodged between two panels as shown. If the rod is to remain in the position shown, determine the maximum allowable acceleration of the system.

16.3 A 6-ft board is placed in a truck with one end resting against a block secured to the floor and the other leaning against a vertical partition. Determine the maximum allowable acceleration of the truck if the board is to remain in the position shown.

200 mm

A

C

B70°

a

Fig. P16.1 and P16.2

A

B

78°

Fig. P16.3

16.4 A uniform rod BC weighing 8 lb is connected to a collar A by a 10-in. cord AB. Neglecting the mass of the collar and cord, deter-mine (a) the smallest constant acceleration aA for which the cord and the rod will lie in a straight line, (b) the corresponding tension in the cord.

16.5 Knowing that the coefficient of static friction between the tires and the road is 0.80 for the automobile shown, determine the maximum possible acceleration on a level road, assuming (a) four-wheel drive, (b) rear-wheel drive, (c) front-wheel drive.

10 in.

14 in.16 in.

B

C

A

PaA

Fig. P16.4

40 in.60 in.

20 in.

G

Fig. P16.5

16.6 For the truck of Sample Prob. 16.1, determine the distance through which the truck will skid if (a) the rear-wheel brakes fail to operate, (b) the front-wheel brakes fail to operate.

16.7 A 20-kg cabinet is mounted on casters that allow it to move freely (m 5 0) on the floor. If a 100-N force is applied as shown, deter-mine (a) the acceleration of the cabinet, (b) the range of values of h for which the cabinet will not tip.

16.8 Solve Prob. 16.7, assuming that the casters are locked and slide on the rough floor (mk 5 0.25).

100 N

h

G

0.6 m

0.9 m

Fig. P16.7

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1045Problems 16.32 The flywheel shown has a radius of 500 mm, a mass of 120 kg, and a radius of gyration of 375 mm. A 15-kg block A is attached to a wire that is wrapped around the flywheel, and the system is released from rest. Neglecting the effect of friction, determine (a) the acceleration of block A, (b) the speed of block A after it has moved 1.5 m.

16.33 In order to determine the mass moment of inertia of a flywheel of radius 600 mm, a 12-kg block is attached to a wire that is wrapped around the flywheel. The block is released and is observed to fall 3 m in 4.6 s. To eliminate bearing friction from the computation, a second block of mass 24 kg is used and is observed to fall 3 m in 3.1 s. Assuming that the moment of the couple due to friction remains constant, determine the mass moment of inertia of the flywheel.

16.34 Each of the double pulleys shown has a mass moment of inertia of 15 lb ? ft ? s2 and is initially at rest. The outside radius is 18 in., and the inner radius is 9 in. Determine (a) the angular acceleration of each pulley, (b) the angular velocity of each pulley after point A on the cord has moved 10 ft.

A m

Fig. P16.32 and P16.33

A A A A

160 lb

(1) (2) (3) (4)

160 lb 460 lb 300 lb 80 lb

Fig. P16.34

16.36 Solve Prob. 16.35, assuming that the couple M is applied to disk A.

4 in.

A B

C

10 in. 10 in.

M

Fig. P16.35

16.35 Each of the gears A and B weighs 20 lb and has a radius of gyra-tion of 7.5 in.; gear C weighs 5 lb and has a radius of gyration of 3 in. If a couple M of constant magnitude 50 lb ? in. is applied to gear C, determine (a) the angular acceleration of gear A, (b) the tangential force which gear C exerts on gear A.

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PROBLEMS

1063

16.75 Show that the couple IA of Fig. 16.15 can be eliminated by attach-ing the vectors mat and man at a point P called the center of per-cussion, located on line OG at a distance GP 5 k2/r from the mass center of the body.

16.76 A uniform slender rod of length L 5 36 in. and weight W 5 4 lb hangs freely from a hinge at A. If a force P of magnitude 1.5 lb is applied at B horizontally to the left (h 5 L), determine (a) the angular acceleration of the rod, (b) the components of the reaction at A.

G

a

r

ma t

ma n

P

O

Fig. P16.75

C

G

B

A

P

L2

L2

r

Fig. P16.78

A

B

h

L

P

Fig. P16.76

A

A'

lx

w

Fig. P16.80

16.77 In Prob. 16.76, determine (a) the distance h for which the hori-zontal component of the reaction at A is zero, (b) the correspond-ing angular acceleration of the rod.

16.78 A uniform slender rod of length L 5 900 mm and mass m 5 4 kg is suspended from a hinge at C. A horizontal force P of magnitude 75 N is applied at end B. Knowing that r 5 225 mm, determine (a) the angular acceleration of the rod, (b) the components of the reaction at C.

16.79 In Prob. 16.78, determine (a) the distance r for which the hori-zontal component of the reaction at C is zero, (b) the correspond-ing angular acceleration of the rod.

16.80 A uniform slender rod of length l and mass m rotates about a verti-cal axis AA9 with a constant angular velocity V. Determine the tension in the rod at a distance x from the axis of rotation.

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1,5 𝑚 1 𝑚

0,5 𝑚

785 𝑁 80 𝑘𝑔 230 𝑘𝑔 150 𝑘𝑔 40 𝑘𝑔