Quiz01 Div3 Soln
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ME 274 – Spring 2009 Quiz No. 1 – Div 3 Friday, January 16
SOLUTION
Particle P moves along rod OA where OA is rotating about a shaft passing through end O. Let r represent the radial distance from O to P and θ be the angle of rotation of the rod, as shown. At a particular instant in time, the velocity and acceleration of P is known to be:
v P = ( !3er + 4 e" ) ft / sec aP = 0
For this instant when r = 2 ft, determine numerical values r , !! and !!! . for r! , !! Solution
v P = ( !3er + 4 e" ) ft / sec = r! er + r"! e"
#
r! = !3 ft / sec r"! = 4 ft / sec
(
#
)
4 4 "! = = = 2 rad / sec r 2
a P = 0 = !! r ! r"! 2 er + ( r"!! + 2 r!"! ) e" !! r ! r"! 2 = 0
#
r"!! + 2 r!"! = 0
#
#
!! r = r"! 2 = ( 2 ) ( 2 ) = 8 ft / sec 2 2 r!"! ( 2 ) ( !3) ( 2 ) = 6 rad / sec2 "!! = ! =! r 2 2
eθ er
SOLUTION
Particle P moves along rod OA where OA is rotating about a shaft passing through end O. Let r represent the radial distance from O to P and θ be the angle of rotation of the rod, as shown. At a particular instant in time, the velocity and acceleration of P is known to be:
v P = ( !3er + 4 e" ) ft / sec aP = 0
For this instant when r = 2 ft, determine numerical values r , !! and !!! . for r! , !! Solution
v P = ( !3er + 4 e" ) ft / sec = r! er + r"! e"
#
r! = !3 ft / sec r"! = 4 ft / sec
(
#
)
4 4 "! = = = 2 rad / sec r 2
a P = 0 = !! r ! r"! 2 er + ( r"!! + 2 r!"! ) e" !! r ! r"! 2 = 0
#
r"!! + 2 r!"! = 0
#
#
!! r = r"! 2 = ( 2 ) ( 2 ) = 8 ft / sec 2 2 r!"! ( 2 ) ( !3) ( 2 ) = 6 rad / sec2 "!! = ! =! r 2 2
eθ er
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