Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 12.2, Problem 12.92P
Two 2.6-lb collars A and B can slide without friction on a frame, consisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about CD. The two collars are connected by a cord running over a pulley that is attached to the frame at O, and a stop prevents
Fig. P12.92
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A smooth can C, having a mass of 5 kg, is lifted from a feed at A to a ramp at B by a rotating rod. The rod maintains a constant angular velocity of θ˙ = 0.5 rad/s, Neglect the effects of friction in the calculation and the size of the can so that r=(1.2cosθ)m. The ramp from A to B is circular, having a radius of 600 mm.
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Chapter 12 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 12.1 - A 1000-lb boulder B is resting on a 200-lb...Ch. 12.1 - Marble A is placed in a hollow tube, and the tube...Ch. 12.1 - The two systems shown start from rest. On the...Ch. 12.1 - Blocks A and B are released from rest in the...Ch. 12.1 - People sit on a Ferris wheel at points A, B, C,...Ch. 12.1 - Crate A is gently placed with zero initial...Ch. 12.1 - Two blocks weighing WA and WB are at rest on a...Ch. 12.1 - Objects A, B, and C have masses mA, mB, and mC,...Ch. 12.1 - Prob. 12.4FBPCh. 12.1 - Blocks A and B have masses mA and mB,...
Ch. 12.1 - A pilot of mass m flies a jet in a half-vertical...Ch. 12.1 - Wires AC and BC are attached to a sphere that...Ch. 12.1 - A collar of mass m is attached to a spring and...Ch. 12.1 - Prob. 12.9FBPCh. 12.1 - At the instant shown, the length of the boom AB is...Ch. 12.1 - Disk A rotates in a horizontal plane about a...Ch. 12.1 - Pin B has a mass m and slides along the slot in...Ch. 12.1 - Prob. 12.1PCh. 12.1 - Prob. 12.2PCh. 12.1 - Prob. 12.3PCh. 12.1 - Prob. 12.4PCh. 12.1 - Prob. 12.5PCh. 12.1 - Prob. 12.6PCh. 12.1 - A tugboat pulls a small barge through a harbor....Ch. 12.1 - Prob. 12.8PCh. 12.1 - 12.9 If an automobile’s braking distance from 90...Ch. 12.1 - Prob. 12.10PCh. 12.1 - The coefficients of friction between the load and...Ch. 12.1 - A light train made up of two cars is traveling at...Ch. 12.1 - Prob. 12.13PCh. 12.1 - Prob. 12.14PCh. 12.1 - Prob. 12.15PCh. 12.1 - Prob. 12.16PCh. 12.1 - A 5000-lb truck is being used to lift a 1000-lb...Ch. 12.1 - Block A has a mass of 40 kg, and block B has a...Ch. 12.1 - Block A has a mass of 40 kg, and block B has a...Ch. 12.1 - The flat-bed trailer carries two 1500-kg beams...Ch. 12.1 - 12.21 A baggage conveyor is used to unload luggage...Ch. 12.1 - To unload a bound stack of plywood from a truck,...Ch. 12.1 - To transport a series of bundles of shingles A to...Ch. 12.1 - An airplane has a mass of 25 Mg and its engines...Ch. 12.1 - Prob. 12.25PCh. 12.1 - A constant force P is applied to a piston and rod...Ch. 12.1 - A spring AB of constant k is attached to a support...Ch. 12.1 - Block A has a mass of 10 kg, and blocks B and C...Ch. 12.1 - Prob. 12.29PCh. 12.1 - Prob. 12.30PCh. 12.1 - A 10-lb block B rests as shown on a 20-lb bracket...Ch. 12.1 - Knowing that k = 0.30, determine the acceleration...Ch. 12.1 - Knowing that k = 0.30, determine the acceleration...Ch. 12.1 - Prob. 12.34PCh. 12.1 - Block B of mass 10 kg rests as shown on the upper...Ch. 12.1 - Prob. 12.36PCh. 12.1 - Prob. 12.37PCh. 12.1 - Human centrifuges are often used to simulate...Ch. 12.1 - A single wire ACB passes through a ring at C...Ch. 12.1 - Prob. 12.41PCh. 12.1 - Prob. 12.42PCh. 12.1 - Prob. 12.43PCh. 12.1 - Prob. 12.44PCh. 12.1 - During a high-speed chase, a 2400-lb sports car...Ch. 12.1 - An airline pilot climbs to a new flight level...Ch. 12.1 - The roller-coaster track shown is contained in a...Ch. 12.1 - A spherical-cap governor is fixed to a vertical...Ch. 12.1 - A series of small packages, each with a mass of...Ch. 12.1 - 12.50 A 54-kg pilot flies a jet trainer in a...Ch. 12.1 - Prob. 12.51PCh. 12.1 - A curve in a speed track has a radius of 1000 ft...Ch. 12.1 - Tilting trains, such as the Acela Express that...Ch. 12.1 - Prob. 12.54PCh. 12.1 - A 3-kg block is at rest relative to a parabolic...Ch. 12.1 - Prob. 12.56PCh. 12.1 - A turntable A is built into a stage for use in a...Ch. 12.1 - The carnival ride from Prob. 12.51 is modified so...Ch. 12.1 - Prob. 12.59PCh. 12.1 - Prob. 12.60PCh. 12.1 - A small block B fits inside a slot cut in arm OA...Ch. 12.1 - The parallel-link mechanism ABCD is used to...Ch. 12.1 - Prob. 12.63PCh. 12.1 - A small 250-g collar C can slide on a semicircular...Ch. 12.1 - A small 250-g collar C can slide on a semicircular...Ch. 12.1 - An advanced spatial disorientation trainer is...Ch. 12.1 - The 3-kg collar B slides on the frictionless arm...Ch. 12.1 - A 0.5-kg block B slides without friction inside a...Ch. 12.1 - Pin B weighs 4 oz and is free to slide in a...Ch. 12.1 - Prob. 12.71PCh. 12.1 - Prob. 12.72PCh. 12.2 - A particle of mass m is projected from point A...Ch. 12.2 - A particle of mass m is projected from point A...Ch. 12.2 - Determine the mass of the earth knowing that the...Ch. 12.2 - Show that the radius r of the moons orbit can be...Ch. 12.2 - Communication satellites are placed in a...Ch. 12.2 - Prob. 12.81PCh. 12.2 - The orbit of the planet Venus is nearly circular...Ch. 12.2 - A satellite is placed into a circular orbit about...Ch. 12.2 - The periodic time (see Prob. 12.83) of an earth...Ch. 12.2 - A 500-kg spacecraft first is placed into a...Ch. 12.2 - A space vehicle is in a circular orbit of 2200-km...Ch. 12.2 - Prob. 12.87PCh. 12.2 - Prob. 12.88PCh. 12.2 - Prob. 12.89PCh. 12.2 - A 1-kg collar can slide on a horizontal rod that...Ch. 12.2 - Two 2.6-lb collars A and B can slide without...Ch. 12.2 - A small ball swings in a horizontal circle at the...Ch. 12.3 - A uniform crate C with mass mC is being...Ch. 12.3 - A uniform crate C with mass m is being transported...Ch. 12.3 - Prob. 12.94PCh. 12.3 - Prob. 12.95PCh. 12.3 - A particle with a mass m describes the path...Ch. 12.3 - A particle of mass m describes the parabola y =...Ch. 12.3 - Prob. 12.98PCh. 12.3 - Prob. 12.99PCh. 12.3 - Prob. 12.100PCh. 12.3 - Prob. 12.101PCh. 12.3 - A satellite describes an elliptic orbit about a...Ch. 12.3 - Prob. 12.103PCh. 12.3 - Prob. 12.104PCh. 12.3 - Prob. 12.105PCh. 12.3 - Halleys comet travels in an elongated elliptic...Ch. 12.3 - Prob. 12.109PCh. 12.3 - A space probe is to be placed in a circular orbit...Ch. 12.3 - The Clementine spacecraft described an elliptic...Ch. 12.3 - A space probe is describing a circular orbit of...Ch. 12.3 - Prob. 12.115PCh. 12.3 - A space shuttle is describing a circular orbit at...Ch. 12.3 - Prob. 12.117PCh. 12.3 - A satellite describes an elliptic orbit about a...Ch. 12.3 - Prob. 12.119PCh. 12.3 - Prob. 12.120PCh. 12.3 - Show that the angular momentum per unit mass h of...Ch. 12 - In the braking test of a sports car, its velocity...Ch. 12 - A bucket is attached to a rope of length L = 1.2 m...Ch. 12 - A 500-lb crate B is suspended from a cable...Ch. 12 - The parasailing system shown uses a winch to pull...Ch. 12 - Prob. 12.128RPCh. 12 - Telemetry technology is used to quantify kinematic...Ch. 12 - The radius of the orbit of a moon of a given...Ch. 12 - Prob. 12.131RPCh. 12 - Prob. 12.132RPCh. 12 - Disk A rotates in a horizontal plane about a...
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- A 1.8-kg collar A and a 0.7-kg collar B can slide without friction on a frame, consisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about its vertical axis of symmetry. The two collars are connected by a cord running over a pulley that is attached to the frame at O. At the instant shown, the velocity vA of Collar A has a magnitude of 2.1 m/s and a stop prevents collar B from moving. The stop is suddenly removed and collar A moves toward E. As it reaches a distance of 0.12 m from, the magnitude of its velocity is observed to be 2.5 m/s. Determine at that instant the magnitude of the angular velocity of the frame and the moment of inertia of the frame and pulley system about CD.arrow_forward12.92 Two 2.6-lb collars A and B can slide without friction on a frame, con- sisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about CD. The two collars are connected by a cord running over a pulley that is attached to the frame at O, and a stop prevents collar B from moving. The frame is rotating at the rate 0 = 12 rad/s and r = 0.6 ft when the stop is removed, allowing collar A to move out along rod OE. Neglecting friction and the mass of the frame, deter- mine, for the position r = 1.2 ft, (a) the transverse component of the velocity of collar A, (b) the tension in the cord and the acceleration of collar A relative to the rod OE. D B Fig. P12.92 A Earrow_forwardThe disk D, which has weight W = 15 lb, starts from rest on an incline when the constant moment M is applied to it. The disk is attached at its center to a wall by a spring of constant k = 7 ft/lb. The spring is unstretched when the disk is at its starting position. The disk rolls down the incline without slipping. Take R = 5 ft, 0 = 25° and g = 32.2 ft/s². Use for the moment of inertia of the disk about G, IG: Figure D Part B R M mR² wwww 1 of 1 Part A - Draw a free body diagram of the disk. Indicate which forces and/or couples do work on the disk. Determine the value of the moment M for the disk to stop after rolling down a distance d = 5 ft down the incline. You must use the work-energy theorem to solve this question.arrow_forward
- ASAParrow_forwardMember AB is uniform and has a mass of 150 kg. It is released from rest in the position shown, and the spring has an initial tension of 500 N. When member AB is horizontal it has a clockwise angular velocity of 2.00 rad/s. Calculate the force constant of the spring if the guide blocks A and B are massless.arrow_forwardThe slotted arm OA rotates about a horizontal axis through point O. The 0.18-kg slider P moves with negligible friction in the slot and is controlled by the inextensible cable BP. For the instant under consideration, θ=36∘, ω=θ˙=4.6 rad/s, θ¨=0, and r=0.63 m. Determine the corresponding values of the tension T in cable BP and the force reaction R perpendicular to the slot. The force R is positive if the contact comes from the lower edge of the slot and negative if the contact comes from the top edge.arrow_forward
- The slotted arm OA rotates about a horizontal axis through point O. The 0.18-kg slider P moves with negligible friction in the slot and is controlled by the inextensible cable BP. For the instant under consideration, θ=36∘, ω=θ˙=4.6 rad/s, θ¨=0, and r=0.63 m. Determine the corresponding values of the tension T in cable BP and the force reaction R perpendicular to the slot. The force R is positive if the contact comes from the lower edge of the slot and negative if the contact comes from the top edge. *The answer is not 2.44 and -0.47arrow_forwardRod OA rotates counterclockwise with an angular position - 2t rad, where t is in seconds. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular hoop rod described by the equation r = 1.6cose m. If the total mass of both collars is 0.5 kg and of the rod and hoop are negligible, when = 30° which takes t = ()(180) sec, determine the circumferential acceleration of the collars, ag. [m/s2] (sign sensitive) 6=ki 16 cos 8.arrow_forwardThe slotted arm OA rotates about a horizontal axis through point O. The 0.18-kg slider P moves with negligible friction in the slot and is controlled by the inextensible cable BP. For the instant under consideration, θ=26∘, ω=θ˙=4.6 rad/s, θ¨=0, and r=0.63 m. Determine the corresponding values of the tension T in cable BP and the force reaction R perpendicular to the slot. The force R is positive if the contact comes from the lower edge of the slot and negative if the contact comes from the top edge. *The answer is not 2.44 and -0.47 or 5.96 and 3.51arrow_forward
- The W1= 69.01-lb block shown rests on a smooth plane (coefficient of kinetic friction = 0) with an angle of θ=34∘ from horizontal. It is connected by a flexible inextensible cord that passes around weightless, frictionless pulleys to a support. The W2 =134.93-lb weight is attached as shown. After the system is released from rest, in what distance will the block on the plain attain a speed of 10.0 ft/s?arrow_forward* Incorrect A 2.9-lb slider is propelled upward at A along the fixed curved bar which lies in a vertical plane. If the slider is observed to have a speed of 8.0 ft/sec as it passes position B, determine (a) the magnitude N of the force exerted by the fixed rod on the slider and (b) the rate at which the speed of the slider is changing (positive if speeding up, negative if slowing down). Assume that friction is negligible. 3.1' ACO Answers: N = v= i -0.848 -16.73 lb ft/sec²arrow_forward1. Two children A and B, each having a mass 30kg, sit at the edge of the merry-go-round which is rotating with angular velocity @ = 2 rad/s. Excluding the children, the merry-go-round has a mass 180 kg and a radius of gyration k₂ = 0.8m. Determine the angular velocity of the merry-go-round if A jumps off horizontally in the -n direction (away from the merry-go-gound) with a speed of 3 m/s, measured with respect to the merry-go-round. After A jumps off, B then jumps off horizontally in the +t direction with a speed of 3 m/s, measured with respect to the merry-go-round - what is the merry-go-round's angular velocity now? Neglect friction and the size of each child. 1m 1m B w = 2 rad/sarrow_forward
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