NATIONAL INSTITUTE OF TECHNOLOGY SILCHAR ENGINEERING

Last updated: 6/10/2023

NATIONAL INSTITUTE OF TECHNOLOGY SILCHAR ENGINEERING MECHANICS First Second Semester All Branch COURSE NO ME 101 ASSIGNMENT 25 1 A slender prismatic bar AB is supported in a horizontal position as shown in Fig A At what distance x from the hinge A should the vertical string DE be attached to the bar in order that when it is cut there will be no immediate change in the reaction at 4 Ans x 21 3 2 A homogeneous square plate of weight W and having dimensions a hangs in a vertical plane by two pins A and B as shown in Fig B Calculate and vertical the horizontal components of the reaction at A an instant after the pin at B is removed Ans X 3W 8 Y 5W 8 nive 0 71 FIG C X 3 10 A slender prismatic bar of total length 21 and weight 2W is bent in a right angle at its middle point O and hangs from a hinge at this point as shown in Fig G Find the maximum angular velocity that the bar will acquire if released from rest in the position shown Ans Om 0 621g l W FIG A 11 If the slender prismatic bar AB shown in Fig H is released from rest in the horizontal position and rotates about A under the influence of gravity find the reaction at A as it swings through the vertical positions Ans R 5W 2 C FIG B 7 A horizontal circular disk of uniform thickness radius a and weight W can rotate freely about its vertical geometric axis Fig F Along a circular track of radius r a particle of weight Q is travelling Initially the disk and the particle are rest what angular velocity will the disk acquire if the particle begins to travel along the track with a constant speed v relative to the disk Assume W 10 lb Q 1 lb a 10 in r 6 in v 4 fps Ans u 0 537 sec 3 In Fig C a wood block of weight W 5 lb rests on a horizontal plane and is attached to a fixed hub O by a horizontal string as shown A revolver bullet of weight w 1 oz is fired horizontal into the center of the block in the direction normal to the plane of the figure with velocity v 2 000 fps Calculate the number of revolutions that the block will make around the vertical axis before coming to rest if the coefficient of friction between the block and plane is 1 4 Neglect the dimensions of the block Ans 3 revolutions 777 2 wiffe LTPC 3104 2444 8 Owing to cooling the linear dimensions of a solid homogeneous sphere uniformly rotating about a diameter diminish by 0 1 per cent What effect will this have on the angular velocity of there is no external moment with respect to the diameter of the sphere Ans The angular velocity increases by 0 2 percent B 9 The wheel of a small gyroscope is set spinning by pulling on a string wound around the shaft The moment of inertia of the wheel is 0 045 Ib sec2 in and the diameter of the shaft on which the string is wound is 1 2 in If 36 in of string is pulled off with a constant force of 12 lb what rpm will be imparted to the wheel Ans n 1 324 rpm FIG G FIG F FIG 11 lb at a radius of 1 ft tons Calculate the maximum and minimum force transmitted to the rall when the speed of the locomotive is 60 mph 5 A rotor A initially at rest is suddenly connected to a rotor B having the initial angular velocity by means of a clutch C Fig D What common angular velocity will the two system acquire if the moment of inertia of the system A is la and that of the system B Is Neglect friction in the bearings Ans co la b FIG D 6 A prismatic bar AB of weight W and length 21 carries two balls M and Nof equal weights Wand is rotating with uniform angular velocity con about the vertical Z axis perpendicular to the bar and through its center of gravity Fig E The balls are kept at equal distances from the axis of rotation by f the strings strings What will be the new angular velocity of the system are suddenly cut and owing to centrifugal forces the balls come to the extreme positions P and Q with distances from the axis of rotation equal to The following numerical data are given we 2 sec W 5 lb 212 70 in W 12 lb 21 30 in and 21 45 in Assume in calculation that the mass of the bar is distributed along its axis and the masses of the balls concentrated at their centers Ans 0 520 3 27 sec A S P O 1 FIG E 12 A slender prismatic bar DE of length I and weight W is rigidly attached at its mid point C to a shaft AB and makers therewith an angle a as shown in Fig L Determine the kinetic energy T of the bar of it rotates with constant angular velocity about AB The following numerical data are given W 20 lb 1 40 in a 45 and the uniform angular speed is 200 rpm Ans T 755 in lb 13 A homogeneous slender prismatic bar AB of length and weight Wis hinged at its lower end A and can rotate freely in the vertical plane as shown in Fig J If the bar is released from rest in the unstable position and falls over under the influence of gravity calculate the horizontal component of the reaction at A when 0 30 Ans X 0 225 W AS 4 16 A homogeneous plate 1 ft square is supported in a vertical plane as shown in Fig L a If the pin at B is removed what angular velocity K um will the plate acquire by the time the diagonal AC becomes vertical b Calculate vertical reaction Ra for the instant when the diagonal AC of the square is vertical Ans a co 4 47 rad sec b R 1 44W FIG I lowest position B 2g l 14 What initial angular velocity should be given to the bar AB in Fig J in the top position in order that it will swing through the vertically below A with angular velocity 20 Ans 15 In Fig K a rotor of weight W 386 lb and radius of gyration is 4 in is mounted on a horizontal shaft and set in rotation by a falling weight W 386 lb as shown If the system is released from rest find the velocity of the block after it has fallen through a distance of 10 ft Ans v 11 35 fps FIG J QA W WY PIG K HG L