Engineering Mechanics: Dynamics
8th Edition
ISBN: 9781118885840
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY
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Chapter 5.7, Problem 157P
To determine
The absolute velocity of
The acceleration of
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(30 pts) Problem 1
A thin uniform rod of mass m and length 2r rests in a smooth hemispherical bowl of radius r. A
moment M
mgr
4
is applied to the rod. Assume that the bowl is fixed and its rim is in the
horizontal plane.
HINT: It will help you to find the length l of that portion of the rod that remains outside the
bowl.
M
2r
a) How many degrees of freedom does this system have?
b) Write an equation for the virtual work in terms of the angle 0 and the motion of the
center of mass (TF)
c) Derive an equation for the variation in the position of the center of mass (i.e., Sŕƒ)
a. HINT: Use the center of the bowl as the coordinate system origin for the problem.
d) In the case of no applied moment (i.e., M 0), derive an equation that can be used to
solve for the equilibrium angle of the rod. DO NOT solve the equation
e) In the case of an applied moment (i.e., M
=
mgr
= -) derive an equation that can be used to
4
solve for the equilibrium angle of the rod. DO NOT solve the equation.
f) Can…
Please show all work step by step
Chapter 5 Solutions
Engineering Mechanics: Dynamics
Ch. 5.2 - Prob. 1PCh. 5.2 - The circular sector rotates about a fixed axis...Ch. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - When switched on, the grinding machine accelerates...Ch. 5.2 - The small cart is released from rest in position 1...Ch. 5.2 - The flywheel has a diameter of 600 mm and rotates...Ch. 5.2 - Prob. 8PCh. 5.2 - Prob. 9PCh. 5.2 - The angular acceleration of a body which is...
Ch. 5.2 - The device shown rotates about the fixed z-axis...Ch. 5.2 - Prob. 12PCh. 5.2 - The T-shaped body rotates about a horizontal axis...Ch. 5.2 - Prob. 14PCh. 5.2 - Prob. 15PCh. 5.2 - Prob. 16PCh. 5.2 - The bent flat bar rotates about a fixed axis...Ch. 5.2 - At time t = 0, the arm is rotating about the fixed...Ch. 5.2 - A variable torque is applied to a rotating wheel...Ch. 5.2 - Prob. 20PCh. 5.2 - Prob. 21PCh. 5.2 - Prob. 22PCh. 5.2 - Prob. 23PCh. 5.2 - Prob. 24PCh. 5.2 - Prob. 25PCh. 5.2 - During its final spin cycle, a front-loading...Ch. 5.2 - Prob. 27PCh. 5.2 - Prob. 28PCh. 5.3 - Slider A moves in the horizontal slot with a...Ch. 5.3 - The fixed hydraulic cylinder C imparts a constant...Ch. 5.3 - Prob. 31PCh. 5.3 - At the instant under consideration, the hydraulic...Ch. 5.3 - The hydraulic cylinder D is causing the distance...Ch. 5.3 - The Scotch-yoke mechanism converts rotational...Ch. 5.3 - Prob. 35PCh. 5.3 - The wheel of radius r rolls without slipping, and...Ch. 5.3 - Link OA rotates with a clockwise angular velocity...Ch. 5.3 - Determine the acceleration of the shaft B for θ =...Ch. 5.3 - Prob. 39PCh. 5.3 - Prob. 40PCh. 5.3 - Boom OA is being elevated by the rope-and-pulley...Ch. 5.3 - The hydraulic cylinder imparts a constant upward...Ch. 5.3 - Prob. 43PCh. 5.3 - The rod OB slides through the collar pivoted to...Ch. 5.3 - Prob. 45PCh. 5.3 - Prob. 46PCh. 5.3 - Link OA is given a clockwise angular velocity ω =...Ch. 5.3 - Prob. 48PCh. 5.3 - Derive an expression for the upward velocity v of...Ch. 5.3 - Prob. 50PCh. 5.3 - Show that the expressions v = rω and at = rα hold...Ch. 5.3 - Prob. 52PCh. 5.3 - Prob. 53PCh. 5.3 - Prob. 54PCh. 5.3 - Prob. 55PCh. 5.3 - Prob. 56PCh. 5.3 - Prob. 57PCh. 5.3 - The punch is operated by a simple harmonic...Ch. 5.4 - The right-angle link AB has a clockwise angular...Ch. 5.4 - The uniform rectangular plate moves on the...Ch. 5.4 - The cart has a velocity of 4 ft/sec to the right....Ch. 5.4 - Prob. 62PCh. 5.4 - The speed of the center of the earth as it orbits...Ch. 5.4 - Prob. 64PCh. 5.4 - The circular disk of radius 8 in. is released very...Ch. 5.4 - For a short interval, collars A and B are sliding...Ch. 5.4 - Prob. 67PCh. 5.4 - The magnitude of the absolute velocity of point A...Ch. 5.4 - Prob. 69PCh. 5.4 - Prob. 70PCh. 5.4 - Determine the angular velocity of bar AB just...Ch. 5.4 - For the instant represented, point B crosses the...Ch. 5.4 - Prob. 73PCh. 5.4 - For a short interval, collars A and B are sliding...Ch. 5.4 - Determine the angular velocity of link BC for the...Ch. 5.4 - The elements of a switching device are shown. If...Ch. 5.4 - Determine the angular velocity ωAB of link AB and...Ch. 5.4 - Determine the angular velocity ωAB of link AB and...Ch. 5.4 - The rotation of the gear is controlled by the...Ch. 5.4 - Prob. 80PCh. 5.4 - Prob. 81PCh. 5.4 - The ends of the 0.4-m slender bar remain in...Ch. 5.4 - Prob. 83PCh. 5.4 - Prob. 84PCh. 5.4 - Pin P on the end of the horizontal rod slides...Ch. 5.4 - A four-bar linkage is shown in the figure (the...Ch. 5.4 - The mechanism is part of a latching device where...Ch. 5.4 - The elements of the mechanism for deployment of a...Ch. 5.4 - Prob. 89PCh. 5.4 - Prob. 90PCh. 5.5 - The slender bar is moving in general plane motion...Ch. 5.5 - Prob. 92PCh. 5.5 - Prob. 93PCh. 5.5 - Roller B of the quarter-circular link has a...Ch. 5.5 - Prob. 95PCh. 5.5 - Prob. 96PCh. 5.5 - Prob. 97PCh. 5.5 - At a certain instant vertex B of the...Ch. 5.5 - Prob. 99PCh. 5.5 - Prob. 100PCh. 5.5 - The mechanism of Prob. 5/100 is now shown in a...Ch. 5.5 - Prob. 102PCh. 5.5 - Prob. 103PCh. 5.5 - The switching device of Prob. 5/76 is repeated...Ch. 5.5 - The shaft of the wheel unit rolls without slipping...Ch. 5.5 - Prob. 106PCh. 5.5 - The attached wheels roll without slipping on the...Ch. 5.5 - The mechanism of Prob. 5/77 is repeated here. By...Ch. 5.5 - Prob. 109PCh. 5.5 - Prob. 110PCh. 5.5 - Prob. 111PCh. 5.5 - Prob. 112PCh. 5.5 - Prob. 113PCh. 5.5 - Solve for the speed of point D in Prob. 5/64 by...Ch. 5.5 - Link OA has a counterclockwise angular velocity =...Ch. 5.5 - Vertical oscillation of the spring-loaded plunger...Ch. 5.5 - A device which tests the resistance to wear of two...Ch. 5.5 - Motion of the roller A against its restraining...Ch. 5.5 - In the design of the mechanism shown, collar A is...Ch. 5.5 - Determine the angular velocity ω of the ram head...Ch. 5.6 - For the instant represented, corner C of the...Ch. 5.6 - The two rotor blades of 800-mm radius rotate...Ch. 5.6 - Prob. 123PCh. 5.6 - Determine the angular velocity and angular...Ch. 5.6 - The wheel of radius R rolls without slipping, and...Ch. 5.6 - The 9-m steel beam is being hoisted from its...Ch. 5.6 - The bar of Prob. 5/82 is repeated here. The ends...Ch. 5.6 - Prob. 128PCh. 5.6 - Prob. 129PCh. 5.6 - Prob. 130PCh. 5.6 - Prob. 131PCh. 5.6 - Prob. 132PCh. 5.6 - Prob. 133PCh. 5.6 - The switching device of Prob. 5/76 is repeated...Ch. 5.6 - Prob. 135PCh. 5.6 - Prob. 136PCh. 5.6 - If the wheel in each case rolls on the circular...Ch. 5.6 - Prob. 138PCh. 5.6 - The system of Prob. 5/101 is repeated here. Crank...Ch. 5.6 - Prob. 140PCh. 5.6 - The mechanism of Prob. 5/77 is repeated here. The...Ch. 5.6 - The system of Prob. 5/84 is repeated here. If the...Ch. 5.6 - The shaft of the wheel unit rolls without slipping...Ch. 5.6 - Plane motion of the triangular plate ABC is...Ch. 5.6 - The system of Prob. 5/110 is repeated here. At the...Ch. 5.6 - The velocity of roller A is vA = 0.5 m/s to the...Ch. 5.6 - In the design of this linkage, motion of the...Ch. 5.6 - The mechanism of Prob. 5/112 is repeated here. If...Ch. 5.6 - The bar AB from Prob. 5/74 is repeated here. If...Ch. 5.6 - If the piston rod of the hydraulic cylinder C has...Ch. 5.6 - Prob. 151PCh. 5.6 - Prob. 152PCh. 5.6 - The four-bar linkage of Prob. 5/86 is repeated...Ch. 5.6 - Prob. 154PCh. 5.6 - Prob. 155PCh. 5.6 - Prob. 156PCh. 5.7 - The disk rotates about a fixed axis through O with...Ch. 5.7 - The sector rotates with the indicated angular...Ch. 5.7 - The slotted wheel rolls to the right without...Ch. 5.7 - The disk rolls without slipping on the horizontal...Ch. 5.7 - Prob. 161PCh. 5.7 - An experimental vehicle A travels with constant...Ch. 5.7 - Prob. 163PCh. 5.7 - Prob. 164PCh. 5.7 - The small collar A is sliding on the bent bar with...Ch. 5.7 - Prob. 167PCh. 5.7 - Vehicle A travels west at high speed on a...Ch. 5.7 - Prob. 169PCh. 5.7 - Prob. 170PCh. 5.7 - Prob. 171PCh. 5.7 - Prob. 172PCh. 5.7 - Prob. 173PCh. 5.7 - Prob. 174PCh. 5.7 - Prob. 175PCh. 5.7 - Prob. 176PCh. 5.7 - Prob. 177PCh. 5.7 - Refer to the figure for Prob. 5/177. Car A is...Ch. 5.7 - For the instant represented, link CB is rotating...Ch. 5.7 - The disk rotates about a fixed axis through point...Ch. 5.7 - All conditions of the previous problem remain the...Ch. 5.7 - Prob. 182PCh. 5.7 - Prob. 183PCh. 5.7 - One wheel of an experimental vehicle F, which has...Ch. 5.8 - Prob. 185RPCh. 5.8 - Prob. 186RPCh. 5.8 - Prob. 187RPCh. 5.8 - Prob. 188RPCh. 5.8 - Prob. 189RPCh. 5.8 - Roller B of the linkage has a velocity of 0.75 m/s...Ch. 5.8 - Prob. 191RPCh. 5.8 - Prob. 192RPCh. 5.8 - Prob. 193RPCh. 5.8 - Prob. 194RPCh. 5.8 - Prob. 195RPCh. 5.8 - Prob. 196RPCh. 5.8 - The isosceles triangular plate is guided by the...Ch. 5.8 - Prob. 198RPCh. 5.8 - The hydraulic cylinder C imparts a velocity υ to...Ch. 5.8 - Prob. 200RPCh. 5.8 - The figure illustrates a commonly used...Ch. 5.8 - Prob. 202RPCh. 5.8 - Prob. 203RPCh. 5.8 - Prob. 204RPCh. 5.8 - Prob. 206RPCh. 5.8 - For the slider-crank configuration shown, derive...Ch. 5.8 - Prob. 212RP
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