chap_V_hwk_fall_2010

chap_V_hwk_fall_2010 - gid Body Kinetics HChapter V: Rigid...

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Unformatted text preview: gid Body Kinetics HChapter V: Rigid omework Problems ME 274 Body Kinetics Homework V-7 roblem V-5 Problem V.5 pallet/winch/roller system is used to move crate B of mass M, where the pallet A has a Given: A ass of m. Determine the pallet/winch/roller system is used to move crate B of mass M, where the pallet A has a mass of m. a) maximum winch force that can be applied to the pallet such that the crate does not tip and Find: Determine: a) the maximum winch force that can be applied to the pallet such that the crate does not friction required between the crate and pallet to ensure b) the coefficient of statictip, and b) the coefficient of static friction required between the crate and pallet to ensure that tipping occurs that tipping occurs prior to slip. prior to slip. d1 d1 d2 G d2 B A Use = 4 kg, M parameters 0 your and d = m m. se the following: mthe1following= 65 kg, d1 =in .3 m, analysis: 0.6= 16kg , M = 80kg , d1 = 0.3m and d2 = 0.6m. 2 V-8 Chapter V: Rigid Body Kinetics Homework netics Homework Problems V-6 ME 274 Problem V.6 Given: The center of mass G of the disk shown below (mass m) is offset by a distance e from the of mass G of the disk shown below (mass position shown,aG is directly above O as the wheel rolls without slip geometric center O. At the m) is offset by distance e from the center O. If Gthrough the bottom of a as the wheel rolls without slip through is in the position shown circular path shown. of a circular path shown, find the normal force N that is exerted by the path on Find: For this position, determine the normal force N that is exerted by the path on the disk. C ! R e O G r Use the following e = 0.05 m, ! = 3 analysis: R = 1. m, llowing: R = 1.25 m, r = 0.25 m, parameters in yourrad/s, and m = 505kg. r = 0.2m, e = 0.1m, ω = 4rad/sec and m = 75kg . Problem V-9 A thin, homogeneous bar AB (having a length of L and mass m) is pinned to ground at pointChapter V: Rigid a distance of L/4 from end A). A homogeneous disk of mass M O (where O is at Body Kinetics Homework and radius r is welded to the bar AB with end B being at the center of the disk. A constant forceProblemend A in such a way that the line of action of F is always perpendicular to F acts at V.9 OA. At instant “1”, the system is released from rest with AB being horizontal. V-11 Given: A thin, homogeneous bar system made up of of L and mass m) is pinned to ground at a) Draw a free body diagram of theAB (having a lengthbar AB and the disk. List point O (where O is at a distance of L/4 from end A). A homogeneous disk of mass M and radius r which, if any, nonconservative forces do work on this system. is welded to the bar AB with end B being at the center of the disk. A constant force F acts at end b) Determine thethat the velocity of bar ABis always perpendicular to OA. The system is released A in such a way angular line of action of F when AB reaches its vertical position (instant “2”). Note that since the from rest with AB being horizontal.disk is welded to AB, the disk has the same angular velocity as bar AB. Find: For this problem: a) determine the angular disk as particle of mass M reaches c) Repeat your calculations in b) but here treat the velocityaof bar AB when AB (that its vertical position, and b) ! 0 is, consider r repeat your calculations in a) but here treat the disk as a particle of mass M. ). F M r m A L/4 O 3L/4 B g VERTICAL PLANE Use the following parameters in your analysis: L = rs r 1 1 e m = 40kg , , Use the following parameters in your analysis: L = 2.5 mete3m,, r == mmt,er , m = 40 kgM = 50kg and M = F = g and. F = 100 Newtons . 50 k 100N Chapter V: Rigid Body Kinetics Homework V-13 Problem V.11 Given: ConsiderBody Kinetics Homework Problems Rigid the three systems (each of total mass m) shown below where: (I) 274 ME made up on a particle of mass m supported within a massless ring by massless spokes, (II) made up of identical, P total mass thin spokes of roblem V-11 m in a massless ring, and (III) a thin ring of mass m. Each system is Consider the three systems (each of total mass m) shown below where: (I) made up on a released from prest, with eachssystem rolling withoutring by massless spokes, (II) made up of article of mass m upported within a massless slipping on a rough incline. identical, thin spokes of total mass m in a massless ring, and (III) a thin ring of mass m. Each the velocity of the mass center O of each system when each system has made Find: Determine system is released from rest, with each system rolling without slipping on a rough ncline. Determine the velocity of the inclines. Rank the speeds of O system two complete irevolutions in rolling down the mass center O of each system when eachfor the three systems. has made two complete revolutions in rolling down the inclines. Rank the speeds of O for Explain in words why the speeds endwords why those rankings.with those rankings. up with the speeds end up the three systems. Explain in g O O R no slip ! (I) massless ring, massless spokes and particle of mass m O R R no slip ! (II) massless ring and identical spokes (with total mass of spokes m) no slip ! (III) thin ring of mass m Chapter V: Rigid Body Kinetics Homework V-17 Rigid Body KineticsProblemProblems Homework V.15 ME 274 Given: The center of the homogeneous disk of mass m shown below has an initial velocity of v0 Problem V-15 up the slope. The center of the homogeneous disk of mass m shown below has an initial velocity of v0 Find: Find the of the of the disk after an elapsed time of ∆t, assuming that up the slope. Find the velocityvelocitydisk after an elapsed time of !t, assuming that the the disk rolls without slip. disk rolls without slip. O r ! ◦ Use m 8 kg, r = 0.3 m, ! = in your analysis: / = and Use the following: the=following parameters 36.87°, v0 = 36 m msec 10kg ,!rt = 105secs . = 30 , v0 = 30m/sec and = 0. m , θ ∆t = 12sec. V-20 Body Kinetics Homework Problems Problem V.18 Chapter V: Rigid Body Kinetics Homework ME 274 blem V-18 Given: The slender bar, shown below, of mass m and length L has a downward velocity vG at the instant shown. Assume that the pivot at the end of bar becomes attached to the support after slender bar, shown below, of mass m and length L has a downward velocity at the falling h. nt shown. Assuming that the pivot at the end of bar becomes attached to the support falling h, determine the angular the angular the bar immediately after impact. Find: Determine velocity of velocity of the bar immediately after impact. Use the following parameters in your analysis: m = 4kg , L = 0.4m, vG = 3m/sec and h = 4m. the following: m = 3 kg, L = 0.3 m, vG = 4 m/s and h = 3 m. V-24 etics Homework Problems Problem V.22 -22 (6/109) Chapter V: Rigid Body Kinetics Homework ME 274 Given: A slender, homogeneous bar of mass m is released from rest. omogeneous bar of mass m is released from rest. Determine the contact force Find: Determine the contact force on the bar due to the smooth horizontal surface on release. ue to the smooth horizontal surface. V-26 Chapter V: Rigid Body Kinetics Homework Problem V.24 mework Problems 6/117) Given: A constant frictional torque Mf from the bearings at O resist the motion of the pulley ME downward with a speed of v . system shown. The system is released with A traveling 274 A1 Find: Determine the speed of block A after it drops through a distance of d. nal torque M f from the bearings at O of the pulley system shown. If the with A traveling downward with a ermine the speed of block A after it istance of d. m, kO A Use the following parameters in your analysis: m = 12kg , Mf = 3N m, vA1 = 0.3m/sec, d = 1.5m and kO = 210mm. parameters in your analysis: m = 12 kg , M f = 3 N ! m , d = 1.5 meters and kO = 210 mm . Chapter V: Rigid Body Kinetics Homework V-37 Rigid Body Kinetics Homework Problems ME 274 Problem V.35 Problem V-35 Given: Bars OA and AB each have a mass of m and a length of L. B is constrained to move in Bthe horizontal direction only. mass of mMO is appliedof L. B OA at O. The system isin ars OA and AB each have a A couple and a length to link is constrained to move released from rest when thedangle between A couple AB is applied. at O. Theall surfacesreleased from the horizontal irection only. OA and M is θ = θ1 Assume system is are smooth. rest when the angle between OA and AB is !1. Assume all surfaces are smooth. Find: Determine the of point B when ! when Determine the velocity velocity of point B = !2. θ = θ2 . B O ! MO L L g A Use the following parameters for your analysis: mm 10 12kgL = 2 m2.!m= θ 80°, 36.87◦ ,0° = 0 and Use the following parameters in your analysis: = = kg, , L = , 5 1 , 11 = !2 = 3 θ2 and MO 6040m. M = = N Nm. O V-38 Chapter V: Rigid Body Kinetics Homework Rigid Body Kinetics Homework Problems ME 274 Problem V.36 Problem V-36 Given: A uniform, disk (of mass m and radius r) is pinned at is applied to amass O. Force F is A uniform disk (m r) is pinned at its center of mass O. Force F its center of rope applied toaround the disk. The diskthe released from rest.released from rest. Assume that the rope wrapped a rope wrapped around is disk. The disk is does not seconds, After 2 slip on the disk. a) determine the angular velocity of the disk. Find: At time t, determine: a) the angular velocity of the disk, and b) the reaction force components on)theeterminepin O. b d disk at the reaction force components at the pin. r O F Use the following parameters in your analysis: m = 15kg , r = 0.4m, F = 200N and t = 2sec. Use the following parameters for your analysis: m = 10 kg, r = 0.3 m, F = 250 N. Rigid Body Kinetics Homework Problems ME 274 Problem V-49 Chapter V: Rigid Body Kinetics Homework V-51 Given: An inextensible cable connects block B with point A on a rigid, homogeneous disk. At the instant shown, point A is directly above the disk’s center O. Block Problem V.49 B has a mass of m = 40 kg, and the disk has a mass of M = 20 kg. The disk is able to roll without slipping on a rough horizontal surface with C being the Given: An inextensible cable connects block B with point A on a rigid, homogeneous disk. At the contact oint instant shown, pointpA is .directly above the disks center O. Block B has a mass of m, and the disk has a mass of M . The disk is able to roll without slipping on a rough horizontal surface with C Find: If the system is released is released the rest. being the contact point. The system from rest atfromposition shown, find the angular acceleration of the disk. Write your answer as a vector. Find: Determine the angular acceleration of the disk immediately after release. M A R/2 O no slip R C B m Use the following parameters in your analysis: M = 20kg and m = 40kg . inetics Homework Problems ME 274 V-50 V-52 Chapter V: Rigid Body Kinetics Homework Particle B (having a mass of m = 10 kg) initially travels on a smooth HORIZONTAL surfaceV.50 a speed of vB1 = 20 m/sec. This particle strikes Problem with point E on a stationary thin homogeneous bar (having a mass of M = 15 kg), Given: being pinned to ground. The coefficient of restitution with end A of the bar Particle B (having a mass of m) initially travels on a smooth HORIZONTAL surface with a speed of v the This point E is known to be e a stationary thin homogeneous bar (having a mass between the particle and B 1 . bar atparticle strikes point E on = 0.6. Furthermore,of Mcontact surface of the bar beingpoint E is smooth. The coefficient of restitution between the the ), with end A between B and pinned to ground. particle and the bar at point E is known to be e. Furthermore, the contact surface between B and point E is smooth. Determine the angular velocity of the bar immediately after being impacted by the particle. Write your answer as a vector. Find: Determine the angular velocity of the bar immediately after being impacted by the particle. A B d m M L vB1 E ! Use the following parameters in your analysis: L = 3m, d = 2m, m = 10kg , M = 15kg , e = 0.6, θ = 60◦ and vB 1 = 20m/sec. Problem V-51 Given: A homogeneous, thin bar AB (of length L = 3 meters and mass m = 50 kg) is Chapter V: Rigid Body Kinetics Homework pinned to a block at A. The block has a mass of M = 100 kg and is constrained to move along a smooth horizontal surface. A horizontal force F = 200 N is Problem V.51 the bar’s center of mass G at an instant when the bar is vertical and applied to at rest. V-53 Given: A homogeneous, thin bar AB (of length L and mass m) is pinned to a block at A. The block has a this problem, is constrained to move along a smooth horizontal surface. A horizontal Find: For mass of M and force F is) applied to the bar’s centerdiagramsG atthe bar and the block below.vertical and at rest. a Complete the free body of mass for an instant when the bar is b) Determine the angular acceleration of the bar for the instant when the Find: Determine F is angular acceleration of the bar for the instant when the force F is applied to force the applied to the bar. the bar. M g A F G L m B Use the following parameters in your analysis: L = 3m, m = 50kg , M = 100kg and F = 200N . Rigid Body Kinetics Homework Problems ME 274 Problem V-54 Chapter V: Rigid Body Kinetics Homework Given: A drum has a mass of M = 30 kg, outer radius of R = 0.5 m, inner radius of r = 0.25 m, a centroidal radius of gyration of kG = 0.6 m and centroid at the Problem V.54 geometric center G. A cable is wrapped around the inner radius of the drum and is connected to particle A having a mass of m = 10 kg. The cable is also Given: A drum has aover an ideal pulley.radius of R, stiffness K = 100 ,N/m is attached wrapped mass of M , outer A spring of inner radius of r a centroidal radius of gyration of kGbetween G of at the geometric center G. A cable is released from rest with theradius and centroid the drum and ground. The system is wrapped around the inner of the drum and is connected to particle A having a mass of m. The cable is also wrapped over an spring unstretched. V-56 ideal pulley. A spring of stiffness K is attached between G of the drum and ground. The system is released from rest with the spring unstretched. Find: Determine the speed of A after it has dropped 2 meters. Find: Determine the speed of A after it has dropped through a distance of d. pulley has negligible mass M R K r G no slip m A Use the following parameters in your analysis: M = 30kg , m = 10kg , R = 0.5m, r = 0.25m, kG = 0.3m, K = 100N/m and d = 2m. Rigid Body Kinetics Homework Problems ME 274 V-60 Chapter V: Rigid Body Kinetics Homework Problem V-58 Given: Link AB (having a mass of m with uniform mass distribution and length L) is Problem V.58 supported by a vertical cable OA (of length 0.6L and negligible mass) at A, and end B is constrained to move within a smooth slot, as shown below. The Given: Link AB (having a mass of m with uniform mass distribution and length L) is supported bar is released from rest when it is horizontal. by a vertical cable OA (of length 0.6L and negligible mass) at A, and end B is constrained to move within a smooth slot, as shown below. The bar is released from rest when it is horizontal. Find: Determine the angular acceleration of AB on release. Use the following parameters: m = acceleration of meters. Find: Determine the angular40 kg and L = 2AB on release. g O 0.6 L massless cable m, L B A ! smooth Use the following parameters in your analysis: m = 40kg and L = 2m. Rigid Body Kinetics Homework Problems V-62 Problem V-60 M Chapter V: Rigid Body Kinetics Homework Given: The compound wheel shown rolls without slipping up the incline on its hub and is pulled by a constant force T = 100 N applied to a cord wrapped arou Given: The compound wheel shown rollsouter rim. The wheel starts from rest, hubs and is of m = 40 kg, and has its without slipping up the incline on its has a mass pulled by a constant force T applied to a cord wrappedgaround its outer rim. The mass O of kOfrom.15 meters. Assume radius of yration about its center of wheel starts = 0 rest, has a mass of m, and has a radius of gyration about not center of mass O of kO . Assume that the the cable does its slip on the wheel. Problem V.60 cable does not slip on the wheel. F velocity The angular after its center wheel after itsacenter O hasd up 2 meters up Find: Determine the angularind: of the wheel velocity of the O has moved distance of moved incline. the incline. F no slip R/2 O R ! Use the following parameters in your analysis: m = 40kg , R = 0.2m, d = 2m, T = 100N and kO = 0.15m. ...
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