Quiz02 Div1 Soln

ME 274 – Spring 2009 Quiz No. 2 – Div 1 Wednesday, January 28

SOLUTION

Corner A of a triangular plate ABC is moving to the left along a horizontal guide with a speed of vA while the plate has a CCW angular velocity of ω. At the instant shown,

A vA

• edge AC is horizontally oriented

0.5 m

• vA = 8 m/sec with vA decreasing at a rate of 72 m/sec2 • ω = 12 rad/sec with ω increasing at a rate of 4 rad/ sec2

C 0.5 m

0.5 m

ω At the instant shown,

y

a) find the velocity vector of corner C, vC

B

b) find the acceleration vector of corner C, aC c) make sketches of vC and aC

x

Solution

vC = v A + ! " r C / A

aC

= vA i + (! k ) " ( 0.5i ) = vA i + 0.5! j

(

vC

)

= #8 i + 0.5 (12 ) j = #8 i + 6 j m / sec aC = a A + ! " r C / A # $ 2 r C / A

vA

= aA i + (! k ) " ( 0.5i ) # $ 2 ( 0.5i )

(

)

= aA # 0.5$ 2 i + 0.5! j

(

)

( )

= 72 # 0.5 (12 ) i + 0.5 ( 4 ) j = 2 j m / sec 2 2

A aA

C