Quiz02 Div3 Soln

ME 274 – Spring 2009 Quiz No. 2 – Div 3 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 A instant shown, • edge AB is vertically oriented • vA = 6 m/sec with vA increasing at a rate of 72 m/sec2

vA 0.5 m

• ω = 12 rad/sec with ω increasing at a rate of 44 rad/ sec2

C

0.5 m

At the instant shown,

ω

a) find the velocity vector of corner B, vB

0.5 m

b) find the acceleration vector of corner B, aB c) make sketches of vB and aB B y

Solution

v B = v A + ! " r B/ A

(

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

)

x

= ( #6 + 0.5 (12 )) i = 0

a B = a A + ! " r B/ A # $ 2 r B/ A

(

)

A

(

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

)

aA

vA aB

(

)

= ( #72 + 0.5 ( 44 )) i + 0.5 (12 ) j = #50i + 72 j m / sec 2 2

vB = 0

B