UNIVERSITI TUN HUSSEIN ONN MALAYSIA FINAL EXAMINATION SEMESTER I SESSION 2009/2010

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Wilfrid Lawrence
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1 Aftisse^ UNIVERSITI TUN HUSSEIN ONN MALAYSIA SEMESTER I SESSION 2009/2010 SUBJECT : DYNAMICS SUBJECT CODE : BDA2013 COURSE : 2 BDD DATE : NOVEMBER 2009 DURATION : 2 */ 2 HOURS INSTRUCTION : ANSWER FOUR (4) OUT OF SIX (6) QUESTIONS THIS PAPER CONSISTS OF 8 PAGES

Q1 The large window in Figure Q1 is opened using a hydraulic cylinder AB. The cylinder extends at a constant rate of 0.5 m/s. (a) Relate the coordinate 0 and s using the law of cosines.

2 Q1 The large window in Figure Q1 is opened using a hydraulic cylinder AB. The cylinder extends at a constant rate of 0.5 m/s. (a) Relate the coordinate 0 and s using the law of cosines. (b) (c) Determine the time derivatives of equation obtained in (a). At the instant # = 40, find the value of s from the equation obtained in (a). (d) Calculate the angular velocity, a of the window at the instant 6 = 40. (e) Determine the time derivatives of equation obtained in (c). (f) Calculate the angular acceleration, a of the window at the instant 0 = 40 Q2 The attached wheels roll without slipping on the plates A and B, which are moving in opposite directions as shown in FIGURE Q2. If v A = 60 mm/s to the right and v B = 200 mm/s to the left, determine; (a) the velocity of the center O. (b) the velocity of the point P. Q3 FIGURE Q3 shows the slider A oscillates in the slot about the neutral position 0 with frequency of 2 cycles per second and an amplitude x max of 50 mm so that its displacement in millimeters may be written as x = 50 sin 4nt where t is the time in seconds. The disc, in turn, is set into angular oscillation about O with frequency of 4 cycles per second and an amplitude 0 max = 0.2 rad. The angular displacement is thus given by 6 = 0.2 sin 8nt. Calculate the acceleration of A for the positions ( a ) x = 0 with x positive. ( b ) x = 50 mm.

3 Q4 FIGURE Q4 shows the pendulum which is suspended at point O and consists of two slender rod AB and OC. The slender rods have the mass of 4 kg/m. The disk is fixed at the ends of slender rod OC and it has a density of 6000 kg/m 3 and a thickness of 15mm. The disk has the radius of 300mm while the hole has the radius of 150mm. Determine; (a) The moment inertia of rod OC and BC passing through the end point O. (b) The moment inertia of the disk about the end point O. (c) The pendulum moment of inertia about an axis passing through the pin at O. (d) (e) The location of y of the center of mass G of the pendulum. The pendulum moment of inertia about an axis passing through the mass center G of the pendulum. Q5 A plate shown in FIGURE Q5 is suspended at A and B. Calculate, (a) (b) (c) Mass of the plate. Location of the center of gravity of the plate. Mass moment of inertia of the plate about the center of gravity. (d) Mass moment of inertia of the plate about the point of rotation at A. When the string at B is immediately cut, determine, (e) The angular acceleration of the plate. (f) The horizontal and vertical components of the reaction at pin A.

Q6 The double pulley shown in FIGURE Q6 has a mass of 15 kg and a centroidal radius of gyration of 165 mm. Cylinder A and B are attached to the cords that are wrapped on the pulleys.

4 Q6 The double pulley shown in FIGURE Q6 has a mass of 15 kg and a centroidal radius of gyration of 165 mm. Cylinder A and B are attached to the cords that are wrapped on the pulleys. The coefficient of kinetic friction between block B and the surface is Knowing that system is released from the position illustrated in FIGURE Q6, determine; (a) (b) The velocity of the cylinder A as it strikes the ground The total distance block B moves before coming to rest. (Hints: think about energy method to solve this problem)

5 SEMESTER / SESSION : SEMESTER 1 /2009/10 COURSE : 2 BDD SUBJECT : DYNAMICS CODE SUBJECT : BDA2013 FIGURE Ol - Hydraulic Window A FIGURE Q2 - Rolling Wheel on the Plates

6 SEMESTER / SESSION : SEMESTER 1 / 2009/10 COURSE : 2 BDD SUBJECT : DYNAMICS CODE SUBJECT : BDA 2013 FIGURE Ol - Hydraulic Window FIGURE Q2 - Rolling Wheel on the Plates

7 SEMESTER/ : SEMESTER 1 /2009/10 COURSE : 2 BDD SESSION SUBJECT : DYNAMICS CODE SUBJECT : BDA 2013 FIGURE 03 - Slider 'A' and the Disc. FIGURE 04 - A Pendulum 6

8 SEMESTER/ : SEMESTER 1 /2009/10 COURSE : 2 BDD SESSION SUBJECT : DYNAMICS CODE SUBJECT : BDA 2013 thickness t=0.005 m 0.1 m r density p=7000 kg/m 0.05 m 0.2 m 0.1 m FIGURE 05 - Hanging Plate :l m FIGURE 06 - Double Pulley

$las e V = V,9 v =rco + V a = a r + a e a r =r-0 2 r a 9 =0r + 2& a = a" + a' v = r +w /J (v B ) 1 =m A (v A ) 2 +m B (v B ) 2 I G co x + m{v G ),</,+ 2 JM A dt =I G 0) 2 + m{v G \d 2 -(vj; (O!$

9 SEMESTER / SESSION SEMESTER 1 / 2009/10 COU RSE 2 BDD SUBJECT DYNAMICS CODE SUBJECT : BDA 2013 s = s 0 +v 0 t + at v = v 0 + at v 2 = VQ + las 1 7 6> = 6> + cot + -at l co = G) 0 + at co 2 = col + las e V = V,9 v =rco + V a = a r + a e a r =r-0 2 r a 9 =0r + 2& a = a" + a' v = r +w /J (v B ) 1 =m A (v A ) 2 +m B (v B ) 2 I G co x + m{v G ),</,+ 2 JM A dt =I G 0) 2 + m{v G \d 2 -(vj; (O! =( v J' 2 Y j M g =I g cc ^ F = ma V = /> V + />' V P/0;ty v /> =(rw = Oxr + (r)'oxy a /< = a r + a p/o^ + a a P = Qx(Qxr)+Qxr + 2(q x (r) 0^)+(r) Oxy - mk G a" =rco 2 =- n =ra t 1+ u^2=t 2 t x +v x =t 2 +v 2 U = AT + AV g + AV e AT = ^m(v 2 2-v 2 ) +^I G (co 2 2-co 2 ) A V g =mg{h 2 -h } ) AV e =±k(x 2 2-xf) h wv, + ^T Jf<# = mv 2 'i = ^r 2 dm, _I 2 XT ~~ -"IT ~ ^ zz 1 2 = mr xv yy 12 1 #2 XX -m(b 2 +C 2 ) 12 yy 12 m r ikz (H 0 \+Y J ]M 0 dt = {H 0 ) 2 zz 12

SOLUTION di x = y2 dm. rdv. m = a 2 bdx. = 2 3 rpab2. I x = 1 2 rp L0. b 4 a1 - x2 a 2 b. = 4 15 rpab4. Thus, I x = 2 5 mb2. Ans.

SOLUTION di x = y2 dm. rdv. m = a 2 bdx. = 2 3 rpab2. I x = 1 2 rp L0. b 4 a1 - x2 a 2 b. = 4 15 rpab4. Thus, I x = 2 5 mb2. Ans. 17 4. Determine the moment of inertia of the semiellipsoid with respect to the x axis and express the result in terms of the mass m of the semiellipsoid. The material has a constant density r. y x y a