Indian Institute of Technology Kharagpur %28IIT-K%29 2008 B.Tech Mechanical Engineering Dynamics - Question Paper
ques. Paper Attached .
INDIAN INSTITUTE OF TECHNOLOGY, Kharagpur Date: / /2007*WSI/AN Autumn End Semester 2007 Time: 3 hrs Full Marks: 60 Dept.: 2nd yr UG+DD ME/MF/PH/EE Subject Name: Dynamics Subject No.: ME20001 All questions carry equal marks. State andjustify any assumptions made by you in solving a problem.. Question paper has 2 pages. Answer any 6 questions
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In the arrangement shown in figure 1, a cylinder of mass m and radius r is always kept in 'contact with the circular enclosure of radius R by means of a preloaded spring which exerts a constant force F0. At the instance when & =0, the center of the cylinder is given an initial velocity of / v0 and released. The entire arrangement is on a horizontal plane. Hence gravitational effects do
S not affect the dynamics. The ball starts sliding initially. Find the time that will elapse before rolling takes place.
A semicircular disc of mqss m and radius ; is placed at the midpoint P of a horizontal simply supported beam as shown in figure 2. The center of gravity of the disc is. at G and the center is at O where OG=4r/3n. The coefficient of friction in one case is 0.8 and in another 0.2. Find, at the initial instant, when the disc is released, the difference in the reaction forces at the pinned end and the roller end in the two cases. '
3. A massless rod with two pins at the ends of mass 1 kg each slides along the channel shown in figure 2. The arrangement is on a horizontal plane. At the instant shown a force F is applied on the pin at A such that it starts moving with a uniform velocity of 1m/s and no acceleration Find F, given R=1m.
4. The slider crank mechanism shown in fiqnr-A.lies nn a horizontal plane. Friction is absent. The radinsnf gyration fif link OA abnut O k 5nn mm Tho mont iwpH to rotate the crank is Mr, = 40GNm. Mass of link OA - m0A - 40 kg. Mass of iink BC -mar = 20 ko. Mass of the slider is m* - 5 kg. Other dimensions are as shown in the figure. Find the relative velocity of the slider when 6
The motion is started from rest at 0= 0.
Two masses are attached to the ends of a tuning fork as shown in figure 5. The fork is forced rotate about the y axis with a constant angular velocity :$. During rotation of the fork the masses oscillate in the rotating xy plane so that xt = r + A sin (pt) x2 = -{r + A sin (pt)}
Neglecting mass of the fork, determine the moment M0 necessary to rotate the system at the constant angular velocity coy.
6. An advertising panel of mass m = 50 kg, length 2a = 2.4 m and width 2b = 1.5 m is kept rotating at a constant rate oh about its horizontal axis by a small electric motor attached at A to frame ACB. The frame itself is kept rotating a constant rate qj? about a vertical axis by a second motor attached at C to the column CD. The panel and the frame complete a full revolution in 6 sc and 12 sec respectively. Shoythat Ihfi dynamic reaction_at P is independent of the length 2a.of the panel and that the ratio /tf//W2 magnitudes of the couples fprfpd hy thp motors A and
C, respectively, is independent of the dimensions and maoo of the-panel and is equai teg)2/z>? at any given instant.
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