Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 19.4, Problem 6RP
To determine
The angular velocity
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In the helicopter shown; a vertical tail propeller is used to pre-
vent rotation of the cab as the speed of the main blades is
changed. Assuming that the tail propeller is not operating
determine the final angular velocity of the cab after the speed
of the main blades has been changed from I80 to 240 rpm. (The
speed of the main blades is measured relative to the cab, and
the cab has a centroidal moment of inertia of 650 lb.ft.s2.
Each of the four main blades is assumed to be a slender rod 14 ft weighing 55 lb.)
The differential pulley C, which rotates as a unit, has a mass of 14.1 kg, an inner radius of 75 mm, an outer radius of 150 mm, and a radius of gyration of 100 mm about its stationary centre of gravity at O. Each cylinder (A and B) has a mass of 18.6 kg. At the instant shown, the light cables do not slip and cylinder A has a velocity of vA= 2.5 m/s (downwards). The motion occurs in a vertical plane. What is the total kinetic energy of the system at this instant? Choose the correct answer.
a) 78.4 Joule
b) 87.6 Joule
c) 73.8 Joule
d) 55.3 Joule
e) 92.2 Joule
The rod AB has a mass of 20 kg,the mass of the piston A and B are both 5kg. Piston B is attached to a spring of constant k = 1200 N/m. The spring is un-stretched when θ = 0. If the rod is released from rest whenθ = 45°
Please find÷
(1) the moment inertia of the rod AB about its mass center G
(2)The angular velocity of rod AB at θ = 0°
(3)the velocity of piston A at θ = 0°
(4) the velocity of Piston B at θ = 0°
(hint: regard the piston A, B, rod as a system, during the motion, except the spring, the weight of rod AB, the weight of pistonB also does work). g = 9.8 m/s2
Chapter 19 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 19.2 - Determine the angular momentum of the 100-kg disk...Ch. 19.2 - Determine the angular impulse about point O for t...Ch. 19.2 - The 60-kg wheel has a radius of gyration about its...Ch. 19.2 - Prob. 2FPCh. 19.2 - Prob. 3FPCh. 19.2 - Gears A and B of mass 10 kg and 50 kg have radii...Ch. 19.2 - The 50-kg spool is subjected to a horizontal force...Ch. 19.2 - Prob. 6FPCh. 19.2 - The rigid body (slab) has a mass m and rotates...Ch. 19.2 - Prob. 2P
Ch. 19.2 - Show that if a slab is rotating about a fixed axis...Ch. 19.2 - The 40-kg disk is rotating at = 100 rad/s. When...Ch. 19.2 - Prob. 5PCh. 19.2 - Prob. 6PCh. 19.2 - The double pulley consists of two wheels which are...Ch. 19.2 - Prob. 8PCh. 19.2 - Prob. 9PCh. 19.2 - The 30-kg gear A has a radius of gyration about...Ch. 19.2 - The pulley has a weight of 10 lb and may be...Ch. 19.2 - Prob. 12PCh. 19.2 - Prob. 13PCh. 19.2 - The rod of length L and mass m lies on a smooth...Ch. 19.2 - Prob. 15PCh. 19.2 - Prob. 16PCh. 19.2 - Prob. 17PCh. 19.2 - The 4-kg slender rod rests on a smooth floor If it...Ch. 19.2 - The double pulley consists of two wheels which are...Ch. 19.2 - The 100-kg spool is resting on the inclined...Ch. 19.2 - Prob. 21PCh. 19.2 - The two gears A and B have weights and radii of...Ch. 19.2 - Prob. 23PCh. 19.2 - The 30-kg gear is subjected to a force of P =...Ch. 19.2 - The 30-lb flywheel A has a radius of gyration...Ch. 19.2 - Prob. 26PCh. 19.2 - Prob. 27PCh. 19.2 - Prob. 28PCh. 19.4 - The turntable T of a record player has a mass of...Ch. 19.4 - The 10-g bullet having a velocity of 800 m/s is...Ch. 19.4 - Prob. 31PCh. 19.4 - Prob. 32PCh. 19.4 - Prob. 33PCh. 19.4 - Prob. 34PCh. 19.4 - The 2-kg rod ACB supports the two 4-kg disks at...Ch. 19.4 - The satellite has a mass of 200 kg and a radius of...Ch. 19.4 - Disk A has a weight of 20 lb. An inextensible...Ch. 19.4 - The plank has a weight of 30 lb, center of gravity...Ch. 19.4 - The 12-kg rod AB is pinned to the 40-kg disk. If...Ch. 19.4 - A thin rod of mass m has an angular velocity o...Ch. 19.4 - Prob. 41PCh. 19.4 - Prob. 42PCh. 19.4 - Prob. 43PCh. 19.4 - Prob. 44PCh. 19.4 - The 10-lb block is sliding on the smooth surface...Ch. 19.4 - Prob. 46PCh. 19.4 - The pendulum consists of a 15-kg solid ball and...Ch. 19.4 - Prob. 48PCh. 19.4 - The 20-kg disk strikes the step Without...Ch. 19.4 - The solid ball of mass m is dropped with a...Ch. 19.4 - Prob. 52PCh. 19.4 - The wheel has a mass of 50 kg and a radius of...Ch. 19.4 - Prob. 54PCh. 19.4 - Prob. 55PCh. 19.4 - Prob. 56PCh. 19.4 - Prob. 57PCh. 19.4 - Prob. 58PCh. 19.4 - The cable is subjected to a force of P = (10t2)...Ch. 19.4 - Prob. 2RPCh. 19.4 - The tire has a mass of 9 kg and a rad1us of...Ch. 19.4 - Prob. 4RPCh. 19.4 - The spool has a weight of 30 lb and a radius of...Ch. 19.4 - Prob. 6RPCh. 19.4 - Prob. 7RPCh. 19.4 - Prob. 8RP
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- A cable is wrapped around the spool’s center hub. The mass of the spool is m= 100 kg, the radius r1 = 0.4 m, r2 =0.6 m, and the radius of gyration is kG = 0.3 m. A horizontal force P = 10 N is applied to the cord. The spool is initially at rest and rolls without slipping. (1) The angular impulse of the spool about point A after 2 second, =________(N·m·s) (two decimal places)arrow_forwardThe two gears A and B have weights and radii of gyration of WA = 15 lb , kA = 0.5 ft and WB = 15 lb , kB = 0.35 ft, respectively. A motor transmits a couple moment to gear B of M=2(1−e−0.5t)lb⋅ft, where t is in seconds. Determine the angular velocity of gear A in t = 5 s , measured counterclockwise, starting from rest.arrow_forwardThe 100-kg spool is resting on the inclined surface for which the coefficient of kinetic friction is μk = 0.11. The radius of gyration about the mass center is kG = 0.26 m Determine the angular velocity of the spool, measured clockwise, when t = 7 s after it is released from rest.arrow_forward
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