For the instant shown, a) determine the angular velocity of link OA. b) determine the speed of D. c) determine the angular acceleration of link OA.

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1 ME 74 Fall 008 PROBLEM NO. 1 Given: mechanism is made up of lins O, B and BD, with all three lins joined at pin. Lin O is pinned to ground at end O, end D of D is constrained to vertical motion only, and end B of B is constrained to horizontal motion only. t the instant shown, lin O is horizontal, lin B is vertical, and end B of B is moving to the right with a CONSTNT speed of v B ft/sec. y x Find: For the instant shown, a) determine the angular velocity of lin O. b) determine the speed of D. c) determine the angular acceleration of lin O. Velocity (1) v = v B +! B " r / B = v B i +! B () v = v O +! O " r /0 +! O (3) v = v D +! D " r / D = v D j +! D Equating (1) and () i : v B! 4" B # " B = v B / 4 = 5rad / sec j : 0 = " O # " O Equating () and (3) i : 4! D "! D j : v D # 3! D " v D ( ) " ( 4 j) = ( v B # 4! B )i ; B ( ) " ( i) = (! O ) j ; O ( ) " (#3i # 4 j) = 4! D i + ( v D # 3! D j) ; D cceleration (4) a = a B +! B " r / B # $ B (5) a = a O +! O " r /O # $ O (6) a = a D +! D " r / D # $ O r / B +! B r /O +! B ( ) " ( 4 j) # $ B ( 4 j) = #4! B i # 4$ B ( ) " ( i) # 0 =! O j ; O ( ) # 0 = a D + 4! D r / D = a D j + (! D ) " #3i # 4 j j ; B ( )i # 3! D j ; D Equating (4) and (5): j :! 4" B ( ) = # O $ # O =! 4 5 =!50 rad / sec $ # O = (!50) rad / sec

2 ME 74 Fall 008 PROBLEM NO. Given: Find: particle P moves in a plane with the path of motion given in terms of its polar coordinates as r =! where r is in meters and θ is in radians. It is nown that P moves in such a way that!r =! 8m / sec = constant. For the position of P corresponding to θ = radians, a) determine the velocity and acceleration vectors (v P and a P ) for particle P. b) determine the rate of change of speed for P. r =! = ( ) = 4 m ( ) ( )( ) d dt :!r =!! "! =!r! = #8 = # rad / sec r P θ d dt : r!! =! +!!!! "!!! = # r!! #!! Therefore, v P =!re r + r!e!! = ("8e r " 8e! )m / sec # ( )(#) ( )( = # rad / sec O ( )e r + ( r!! " +!r!" )e " = (!16e r + 4e " )m / sec a P = r!!! r!"!v P = a P i v P = (!16e r + 4e " ) i v P #!e r! e " & % ( $ ' 16! 4 = =!4 m / sec

3 ME 74 Fall 008 Part (a) 5 points scale drawing of a rigid dis B is shown below along with the paths for points and B on the dis. lso shown is the velocity of where the speed of is nonzero (v > 0 ). Circle the response below that most accurately describes the speeds v and v B : a) v B b) 0 < v B < v c) v B = v > 0 d) v B > v > 0 e) more information is needed to compare the sizes of speeds v and v B. You are not required to show any wor for this problem. However, without supporting calculations or descriptions, no partial credit can be given. The IC for the dis (point C) is at the intersection of the perpendiculars to the velocities of points and B.! dis = v C = v B BC ( ) # " v B = BC & % ( v > v since, from figure we see BC > C $ C ' v B B ω dis C path of B path of v

4 ME 74 Fall 008 Part (b) 5 points Sprinler arm O is pinned to a cart at point O. The cart moves to the right with a speed of v cart with!v cart = ft / sec = constant. Fluid flows through the sprinler arm at a rate of! d with!! d =!3 ft / sec = constant. The sprinler arm is being raised at a constant rate of!! = 4 rad / sec. n observer and corresponding xyz coordinate system are attached to the sprinler arm, as show in the figure below. The following equation is to be used to calculate the acceleration of a pellet P that flows with the fluid: a P = a O + a P/O ( ) +! " r rel P/O + # " ( v P/O ) + # " # " r rel ( P/O ) For this position, provide numerical values for the following VECTORS of the above equation in terms of their xyz components when d = 3 feet, v cart = 3 ft / sec,! d = 5 ft / sec and θ = 90 : a O =!!v cart j =! j ( ) ft / sec! = "! = ( 4) rad / sec! =!! " ( v P/O ) = di! = 5i rel ( ) ft / sec ( a P/O ) = di!! =!3i rel ( ) ft / sec x v cart y d P θ O

5 ME 74 Fall 008 Part (c) 5 points Blocs and B are connected by a single, inextensible cable, with this cable being wrapped around pulleys at and E. ssume the radii of the pulleys to be small. Bloc B moves downward with a speed of v B = 6 ft/sec. Determine the velocity of bloc when s = 4 ft. L = length of cable = s + s s B + constant = constant! dl dt =!s + 1 s!s +!s B! s + 9!s!s = " B 6 = " 1+ s / s / 5 = " 10 / 3 ( ) ft / sec 3 ft E s s B B v B

6 ME 74 Fall 008 Part (d) 5 points The mechanism shown below is made up of rigid lins O, B and BE. Lin O is rotating in the counterclocwise direction with a speed of ω O. a) Determine the location of the instant center for lin B in the figure below. b) Is lin B rotating clocwise or counterclocwise? Explain. c) Is lin BE rotating clocwise or counterclocwise? Explain. ω BE E v B B v ω O ω B O C

ME 274 Spring 2017 Examination No. 2 PROBLEM No. 2 (20 pts.) Given:

ME 274 Spring 2017 Examination No. 2 PROBLEM No. 2 (20 pts.) Given: PROBLEM No. 2 (20 pts.) Given: Blocks A and B (having masses of 2m and m, respectively) are connected by an inextensible cable, with the cable being pulled over a small pulley of negligible mass. Block