fig. p15.156 and p15.157 b u b v p b. o b p 15.159 a o ab,...

DepartamentodeEngenhariaMecânicaÁreaCientíficadeMecânicadosMeiosSólidos

RMM–2015/16

MecânicaAplicada

Cap.151-Movimentorelativocomeixosemrotação

Problema15.160

No instante mostrado na figura, o comprimento da lança𝐴𝐵estásendo diminuído a uma taxa constante de0,18 𝑚/𝑠e a lança estásendobaixadaaumataxaconstantede0,08 𝑟𝑎𝑑/𝑠.Determine:

(a) avelocidadedoponto𝐵;(b) aaceleraçãodoponto𝐵.

Problema15.175

Sabendoqueno instantemostradona figura,abarraarticuladaemB

gira no sentido anti-horário com velocidade angular constante de

𝜔 = 6 𝑟𝑎𝑑/𝑠, determine a velocidade angular e a aceleração angular

dabarraarticuladaemA.

Problema15.170

Ocolar𝑃deslizaparaforacomumavelocidaderelativaconstante𝑢ao

longo da barra𝐴𝐵 , que roda no sentido𝑎𝑛𝑡𝑖 − ℎ𝑜𝑟á𝑟𝑖𝑜 com uma

velocidadeangularconstantede20 𝑟𝑝𝑚.

Sabendo que𝑟 = 25𝑐𝑚 quando𝜃 = 0° e que o colar P chega a B

quando𝜃 = 90°,determinea intensidadedaaceleraçãodocolar𝑃no

momentoexatoemqueeleatingeoponto𝐵.

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

980 Kinematics of Rigid Bodies 15.156 and 15.157 Two rods AE and BD pass through holes drilled into a hexagonal block. (The holes are drilled in different planes so that the rods will not touch each other.) Knowing that at the instant considered rod AE rotates counterclockwise with a con-stant angular velocity V, determine, for the given data, the relative velocity of the block with respect to each rod.

15.156 (a) u 5 90°, (b) u 5 60°. 15.157 u 5 45°.

15.158 Four pins slide in four separate slots cut in a circular plate as shown. When the plate is at rest, each pin has a velocity directed as shown and of the same constant magnitude u. If each pin maintains the same velocity relative to the plate when the plate rotates about O with a constant counterclockwise angular velocity V, determine the acceleration of each pin.

15.159 Solve Prob. 15.158, assuming that the plate rotates about O with a constant clockwise angular velocity V.

15.160 At the instant shown the length of the boom AB is being decreased at the constant rate of 0.2 m/s and the boom is being lowered at the constant rate of 0.08 rad/s. Determine (a) the velocity of point B, (b) the acceleration of point B.

A

B

E

D

H

l

q60°

Fig. P15.156 and P15.157

u

u

u

uOP1

P2

P3

P4

r

rr

r

Fig. P15.158

A

B

q = 30!

6 m

Fig. P15.160 and P15.161

12 in.

5 in.

z

BE

CAF

x

y

12 in.D

u

Fig. P15.162 and P15.163

15.161 At the instant shown the length of the boom AB is being increased at the constant rate of 0.2 m/s and the boom is being lowered at the constant rate of 0.08 rad/s. Determine (a) the velocity of point B, (b) the acceleration of point B.

15.162 and 15.163 The sleeve BC is welded to an arm that rotates about A with a constant angular velocity V. In the position shown rod DF is being moved to the left at a constant speed u 5 16 in./s relative to the sleeve. For the given angular velocity V, determine the acceleration (a) of point D, (b) of the point of rod DF that coin-cides with point E.

15.162 V 5 (3 rad/s) i. 15.163 V 5 (3 rad/s) j.

bee29400_ch15_0914-1023.indd Page 980 12/14/08 9:27:34 AM user-s172bee29400_ch15_0914-1023.indd Page 980 12/14/08 9:27:34 AM user-s172 /Volumes/204/MHDQ077/work%0/indd%0/Volumes/204/MHDQ077/work%0/indd%0

982 Kinematics of Rigid Bodies 15.172 The collar P slides outward at a constant relative speed u along rod AB, which rotates counterclockwise with a constant angular velocity of 20 rpm. Knowing that r 5 250 mm when u 5 0 and that the collar reaches B when u 5 90°, determine the magnitude of the acceleration of the collar P just as it reaches B.

A

B

P

u

ww

q

500 mmr

Fig. P15.172

15.173 Pin P slides in a circular slot cut in the plate shown at a constant relative speed u 5 90 mm/s. Knowing that at the instant shown the plate rotates clockwise about A at the constant rate v 5 3 rad/s, determine the acceleration of the pin if it is located at (a) point A, (b) point B, (c) point C.

A

B

C

Pu

100 mm

ww

Fig. P15.173 and P15.174

15.174 Pin P slides in a circular slot cut in the plate shown at a constant relative speed u 5 90 mm/s. Knowing that at the instant shown the angular velocity V of the plate is 3 rad/s clockwise and is decreasing at the rate of 5 rad/s2, determine the acceleration of the pin if it is located at (a) point A, (b) point B, (c) point C.

15.175 and 15.176 Knowing that at the instant shown the rod attached at B rotates with a constant counterclockwise angular velocity VB of 6 rad/s, determine the angular velocity and angular acceleration of the rod attached at A.

A B

D

30!

0.4 m

Fig. P15.175

A B

D

30!

0.4 m

Fig. P15.176


982 Kinematics of Rigid Bodies 15.172 The collar P slides outward at a constant relative speed u along rod AB, which rotates counterclockwise with a constant angular velocity of 20 rpm. Knowing that r 5 250 mm when u 5 0 and that the collar reaches B when u 5 90°, determine the magnitude of the acceleration of the collar P just as it reaches B.

A

B

P

u

ww

q

500 mmr

Fig. P15.172

15.173 Pin P slides in a circular slot cut in the plate shown at a constant relative speed u 5 90 mm/s. Knowing that at the instant shown the plate rotates clockwise about A at the constant rate v 5 3 rad/s, determine the acceleration of the pin if it is located at (a) point A, (b) point B, (c) point C.

A

B

C

Pu

100 mm

ww

Fig. P15.173 and P15.174

15.174 Pin P slides in a circular slot cut in the plate shown at a constant relative speed u 5 90 mm/s. Knowing that at the instant shown the angular velocity V of the plate is 3 rad/s clockwise and is decreasing at the rate of 5 rad/s2, determine the acceleration of the pin if it is located at (a) point A, (b) point B, (c) point C.

15.175 and 15.176 Knowing that at the instant shown the rod attached at B rotates with a constant counterclockwise angular velocity VB of 6 rad/s, determine the angular velocity and angular acceleration of the rod attached at A.

A B

D

30!

0.4 m

Fig. P15.175

A B

D

30!

0.4 m

Fig. P15.176


5,4 𝑚

fig. p15.156 and p15.157 b u b v p b. o b p 15.159 a o ab,...

Documents