A uniform slender rod of length l. Know that? 255 mm. Express your answer in terms of L and m. Assume the pivot is frictionless. below. 0 In Prob. 78, determine (a) the distance h for which the horizontal A uniform slender rod of length L = 900 mm and mass m = 4 kg is suspended from a pin at C and is at rest. Step 2: Dividing the Rod into Elements. Use the angular position coordinate 0, (a) apply Newton's second law and derive the differential equation of motion, and (b) determine the natural angular frequency, for small oscillations. A uniform slender threaded rod of length L= 1. Step 3: Mathematical Formulation. The uniform slender rod has a mass of 10 kg and the length of L = 10 m. It is originally at rest and held by inextensible-massless cables A and B. B. 7 m, mass m = 2 kg, and I = 1/12 m L^2. Find . With what speed does end A strike the 33° incline? Neglect the small mass and friction of the end rollers. eBook &Resources CONSTRAINEDPLAN EMOTION value: 10. 45 Here’s the best way to solve it. Transcribed image text: A uniform slender rod of length L is dropped onto rigid supports at A and B. At the initial m 6. b. Neglect friction and the mass of the small end roller and find the initial acceleration of A. : 4 mĽÖ + 1 mgL0 =0 ; 0,= 2L M, L The corresponding angular acceleration of the rod is rad/s2 O. Determine the distance r for which the horizontal component of the reaction at C is zero. Integrating from -L/2 to +L/2 from the center includes the entire rod. Question: A collar with a mass of 2 kg is rigidly attached at a distance d=300 mm from the end of a uniform slender rod AB. 2mL 2 /3. The acceleration is positive if down the slope, negative if up the slope. Know that? nd mass m 5. Consider the uniform slender rod of mass m and length L. hinge at C. Determine all inertia components of the uniform, slender rod of mass m and length L shown in Fig Q2. A horizontal force P of magnitude 70 N is applied at end B. The elongation of the rod is. As sketched in the figure below, a uniform slender rod of mass M and length L is suspended via two inextensible cables at locations A and B. 78, determine (a) the distance h for which the horizontal A uniform slender rod of mass m and length l lies in the xy plane inclined to the x-axis by an angle θ. 1 kg. Mechanical Engineering questions and answers. Knowing that "bar" - 225 mm and the resulting angular acceleration of the rod is 151. and weight W= 4. 51. 8]Ib hangs freely from a hinge at A. Slider A is mass-less and friction-less. The rod has a mass of 5 kg and is of length L=400 mm. D : l/2 l/3 t K Question: Chapter 6, Problem 6/068 The uniform slender rod of mass m and length L is released from rest in the inverted vertical position shown. A uniform slender rod of length L = 1140 mm and mass m = 5. 65 L. A uniform slender rod of length L = 1020 mm and mass m = 4. A: А h L P F B Fig. 3). ^ Chegg survey fielded between Sept. Knowing that the rod is released from rest in the position shown, Using the conservation of Energy principle, determine the angular velocity of the rod after it has rotated through 60∘. (Figure 1) If it is released from rest when theta = 0 degree, determine the magnitude of the reactive force exerted on it by pin B when theta = 90 degree. 1 rad/s2, determine the acceleration of the rod's mass center G in m/s2 The uniform slender rod of mass m and length L is released from rest in the inverted vertical position shown. The motion of the uniform slender rod of length L = 0. The disk rotates about a vertical axis with a constant angular velocity w. Chapter 6, Problem 6/068 The uniform slender rod of mass m and length L is released from rest in the inverted vertical position shown. Express your answer in terms of some or all of the variables m, L and standard gravity g. A uniform slender rod of length L = 900 mm and mass m = 4. It is held horizontal and releasaed. The acceleration is positive if down the The uniform slender rod of mass m and length L is initially at rest in a centered horizontal position on the fixed circular surface of radius R = 0. A uniform slender rod of length L = 36 inches and weight W = 4 1b hangs freely from a hinge at A. 00 points Required information Determine the angular acceleration of the rod. (a) the A uniform slender rod of length L, cross sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The system rod-nut is released from rest in the horizontal position. Suggest Corrections. 995 views 3 years ago. Here’s the best way to solve it. ) The vertical component is N and the Question: 16. Use the following: ! = 36. is pinned to the slider A. Step-By-Step Guide For Derivation Of Moment Of Inertia Of An Uniform Rigid Rod. Knowing that F 225 mm, determine (a) the angular acceleration of the rod, (b) the components of the reaction at C. Question: 3. A horizontal force P of magnitude 75 N is applied at end B. 5 ib is applied at B horizontally to the left (h = L). 2 kg is suspended from a hinge at C. A uniform slender rod of length L 1100 mm and mass m- 5 kg is suspended from a hinge at C. ) There are 2 steps to solve this one. Required information NOTE: This is a multi-part question. Aug 22, 2020 · 4. 6 kg. A. If a force P normal to the bar is gradually applied to its end until the bar begins to slip at the angle θ=32∘, determine the coefficient of static friction μs . Evaluate your result for @ = 32%, L = 320 mm, and m = 6. determine the angular velocity of the rod and the velocity of its mass center immediately after the rod (a) strikes support A. Once an answer is submitted, you will be unable to return to this part A uniform slender rod of length L = 1020 mm and mass m= 4. 6/68 The uniform slender rod of mass m and length L is released from rest in the inverted vertical position shown. Since support B is slightly lower than support A. 2. Find the natural frequency of the system if k = 2000 N/m, k t = 1000 N-m/rad, l = 5 m and m = 10 kg, Solution: F. and weight W = 4 lb hangs freely from a hinge at A. Knowing that r=200 mm, determine (a) the angular acceleration of the rod; & (b) the reaction force at C. There are 2 steps to solve this one. 8 lb hangs freely from a. (magnitude and direction and units. 5 lb is applied at B horizontally to the left h = (1/2)L (careful, it is not h=L, determine (a) the angular acceleration of the rod, (b) the components of the reaction at A. Find: (a) Determine the acceleration of the rod's center of mass G; and (b) Determing the rod's angular acceleration. Step 1. D. A particle of mass 2m is fixed at one end of the rod as shown. S. The rod is released from rest in the horizontal position shown Determine the angular velocity of the bar when it passes the vertical position. value Required information 10. VOJA 71 B. 5 1b is applied at B horizontally to the left (h = L), determine a) the angular acceleration of the rod, b) the components of the reaction at A. A uniform slender rod of length L = 1260 mm and mass m = 5. and weight W=4 lb hangs freely from a hinge at A. Given: A uniform slender rod is at rest upon a frictionless horizontal surface when a force F is Rectangular applied in the direction shown. 78 A uniform slender rod is at rest upon a frictionless horizontal surface when a force F is applied in the direction shown. Evaluate your result for θ = 31°, L = 490 mm, and m = 4. 76, determine (a) the distance h for which the hori- A A uniform slender rod of length L=900 mm and mass m=4 kg is suspended from a hinge at C. 7-P8. 키 Determine the angular acceleration of the rod. (Round the final answer to the nearest whole number. Please explain the answer to this and please dont use the solution from the textbook. Consider a uniform slender rod of mass m attached to the spring k which is subjected to a harmonic force F (t) = F o cosΩt as shown. 8 kg. The uniform slender rod of length L and mass m is pivoted at x = L/4. А P B Determine the distance r for which the horizontal component of the reaction at Cis zero. A uniform slender rod of length L is dropped onto rigid supports at A and B. y_0 = l/2 sin theta_0 g = gravity acceleration N = normal force J = 1/12 m l^2 inertia rod moment regarding it's center of mass The dynamics are -m g + N = m ddot y = m l Aug 27, 1995 · Mechanical Engineering questions and answers. 8 kg is suspended from a hinge at C. 87¡, mg = 5 lb, F = 15 lb and L = 2 ft. Problem 16. Share Share. 93 A uniform slender rod of mass m and length / is hinged at point A and is attached to four linear springs and one torsional spring, as shown in Fig. Knowing that the weight of the rod is 10 lb, determine (a) the distance h, (b) the tension in the reaction at B cord, (c) the. P16. A slender uniform rod of length L - 20 in. 102. Question: 8. Question: 2. 76 A uniform slender rod of length L = 900 mm and mass m = 4 kg is suspended from a hinge at C. -1000 Nm/rad m-10kg ; 1. Know that i = 265 mm 10 K 10 Determine components of the reaction at C. If k=4000 N/m,m=10 kg,c1=c2=20 N⋅s/m, and l=5 m, find the complete solution provided that the rod has zero initial angular displacement and an Mar 18, 2018 · N =4/7 m g If the floor is frictionless, the rod center of mass will move in a vertical line until the floor. 5 kg. 5 lb is applied at B horizontally to the left (h=L), determine (a) the angular acceleration of the rod, (b) the components of the reaction at A. If the unit mass of the rod is ρ, and it is rotating at a constant angular velocity of ω rad/sec, show that the total elongation of the rod is ρω2 L 3 /3E. P5-6. Table of Contents. 3: A stationary uniform slender rod, length L=20 (in) and weight W=120 [lb], is supported at point C as shown in figure at distance r-L/5 from point A. Step 1: Conceptualizing the Problem. Consider the two-degree-of-freedom system shown in the Figure, where two uniform slender rods of mass m and length L are connected by a translational spring of stiffness k. Find The natural frequency of To perform the integral, it is necessary to express eveything in the integral in terms of one variable, in this case the length variable r. 5 lb is applied at Bhorizontally to the left (n=). 5 kg is suspended from a hinge at C. The system shown in Fig. 5mL 2 /3 A uniform slender rod of length L = 54 in, and weight W = 5. The mass of the hoop is M. 16. 3g Ans. Calling m = rod mass l = rod length theta = angle with the floor y = l/2 sin theta mass center vertical coordinate. If a force P normal to the bar is gradually applied to its end until the bar begins to slip at the angle θ = 2 8 ∘, determine the coefficient of static friction μ s . If a force P of magnitude 3. Solution. Knowing that r=225 mm, determine (a) the angular acceleration of the rod, (b) the components of the reaction at C. B Determine the angular acceleration of the rod. (You must provide an answer before moving on to the next A uniform slender rod of length L is dropped onto rigid supports at A and B. 2 lb hangs freely from a hinge at A. O 0 -X 5. A uniform slender rod of length L = 1180 mm and mass m = 5. A uniform slender rod of mass m and length l is hinged at point A and is attached to four identical linear springs and one torsional spring, as shown to the right. A uniform slender rod of length l and mass m is secured to a circular hoop of radius l as shown. A uniform slender rod of length L= 980 mm and mass m= 4. Assuming perfectly elastic impact at both A and B, determine the angular velocity of the rod and the velocity of its mass center immediately after rod (a) strikes support A, (b) strikes support B, (c) again Question: Chapter 6, Problem 6/068 The uniform slender rod of mass m and length L is released from rest in the inverted vertical position shown. eBook&Resources CONSTRAINED PLANE MOTION value: 10. Problem 5. The mass of the hoop is negligible. The rod is connected at its center of mass to a linear spring which has a stiffness coefficient k. The rod is attached to a spring and a damper at one end and to a damper at the other end, as shown in the figure. ) The distance is mm. The mass moment of inertia of a slender rod with mass m and length l about its center 4. (Hint: parallel axis theorem. 0. and weight W= 4 lb hangs freely from a hinge at A. the rod strikes A with a velocity 7, before it strikes B. Step 4: Integrating Over the Rod. Expert-verified. Problem #3 (20 points): A uniform slender rod of mass m = 8 kg and length l = 1. pall A uniform slender rod of length L = 44 in. lf a force P of magnitude 1. eBook & Resources CONSTRAINED PLANE MOTION 4. Question: [ 2 ] 2. A uniform slender rod of length L=900 mm and mass m=1 kg hangs freely from a hinge at A. ) A uniform slender rod of mass m and length l is hinged at point O, as shown in Fig. 5 N is applied at B horizontally to the left at h, determine (a) the distance h for which the horizontal component of the reaction A is zero, (b) the angular acceleration of the rod. The angle O formed by the rod is measured from the vertical. 78: A uniform slender rod of length L = 36 inches. 2 kg is attached to the rod as shown in the figure. (You must provide an answer before moving on to the next part. 7. A uniform circular disk of mass m is pivoted at point O, as shown. 076. 00 points Determine the components of the reaction at A. (Figure 1) 2. Created by Chegg. 00 points Determine the angular acceleration of the rod. Evaluate your result for = 349, 2 = 250 mm, and m - 3. Assume the rod is initially at rest and note that gravity acts on the system. = 0. Assuming that the rod has mass m and length of L, determine the (a) acceleration of the rodÕs center of mass G and (b) the rodÕs angular acceleration. End A of a slender, uniform rod of length L and weight W bears on a surface as shown, while end B is supported by a cord BC. 6 kg is suspended from a hinge at C. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that The parallel axis thecrem relates Ie, the moment of inertia of an object The uniform slender rod of length / is welded to the bracket at A on the underside of the disk B. A force F=10. 5 lb is applied at B horizontally to the left (h = L), determine (a) the angular accel- eration of the rod, (b) the components of the reaction at A. (b) strikes support B. Knowing that the horizontal force P of magnitude 75 N is applied at end B, determine (a) the distance r for which the horizontal component of the reaction at C is zero, (b) the corresponding angular acceleration of the rod 19. 75 L. For the following parts of this problem, use the parallel axis theorem: a. 5 m and mass m= 3 kg is guided by pins at A and B that slide freely in frictionless slots, circular and horizontel, cut into a vertical plate. The system is subjected to a harmonic forcing function Ft) Fo sin cort, as shown in the figure. Question 3 50 marks) A uniform slender rod of mass m and length L is hinged at point O, and is attached to four linear springs and one torsional spring, as shown in this Figure. The torques tl and t2 are applied to the pivot points 01 and 02, respectively. D : l/2 l/3 t K Advanced Physics questions and answers. Find the natural frequency of the system if k = 2000 N/m, k_t = 1000 N middot m/rad, m = 10 kg, and l = 5m. A small nut of mass m=0. 16,77 In Prob. 2 [1b) is applied at point B at angle of B=30° A Ir 4/2 G F 1/2 В B Q6: Determine the angular acceleration of the rod, CA (rad/s?)? 16. Assume small oscillation. Express the inertia of the rod at point A. The corresponding angular acceleration of the rod is 163 rad/s2 0. 5 lb is applied at Bhorizontally to the left (h= 2). A uniform slender rod of length `L` and mass `M` is pivoted at one end. Assuming that the coefficient of restitution between the rod and supports is e-0. A horizontal force P of magnitude 75 N is applied at end B Know that 7 285 mm. 13 a) Use Newton's lI law to find the natural frequency of the system, if k= 2000 N/m ; k1= 1000 Nm/rad m= 10 kg ; 1-5m Mass:m Length: L 21 /3 b) Solve the same problem by using Rayleigh's method. Knowing that a horizontal force P of magnitude 75 N is applied at end B, determine (a) the distance r for which the horizontal component of the reaction at C is zero, (b) the corresponding angular acceleration of the rod. டண்-ண்---. 5 m Here’s the best way to solve it. 45, determine (a) the value θ for which motion is impending, (b) the corresponding value of the tension in the cord. 1. A uniform slender rod of length = 1060 mm and mass m - 4. 3. Question: 16. Outline Of Solution. The correct option is D. Evaluate your result for 9 = 339, L = 245 mm, and m = 6. Net elongation of the rod is. Determine the distance for which the horizontal component of the reaction at C is zero. Question: 6/68 The uniform slender rod of A uniform slender rod of length L = 900 mm and mass m = 4 kg is suspended from a hinge at C. A uniform slender rod of length L = 900 mm and mass m = 4 kg is suspended from a. a) Use Newtonsn to find the natural frequency of the kt system, if k= 2000 N/m ; k. Once an answer is submitted, you will be unable to return to this part A uniform slender rod of length L = 48 in, and weight W=5. Determine the corresponding angular acceleration of the rod. A: Obtain the differential equation of motion for θ (t). (3 pts) . Evaluate your result for @ = 200, L = 500 mm, and m = 3. 78 A uniform slender rod of length L = 36 in. Assuming perfectly elastic impact at both A and B, determine the angular velocity of the rod and the velocity of its mass center immediately after rod (a) strikes support A, (b) strikes support B, (c) again A uniform slender rod of length L = 1180 mm and mass m=5. Knowing that r = 225 mm, determine The angular acceleration of the rod at the instant that P is applied. The moment of inertia of the rod about an axis that is perpendicular to the rod and that passes through its center of mass is given by ICM = ml. Upon impact with the support, the point A on the rod becomes attached A uniform slender rod of length L is dropped onto rigid supports at A and B. O1 and O2 are the angular displacements of the rods. Suppose a uniform slender rod has length L and mass M. hinge at A. A uniform slender rod of length L = 900 mm and mass m = 4 kg is suspended from a hinge at C. 5 lb is applied at B horizontally to the left h = (1/2)L (careful, not h=L), determine (a) the angular acceleration of the rod, (b) the components of the reaction at A. In the figure below, a uniform slender rod of length L = 0. The uniform slender rod of mass m and length L is initially at rest in a centered horizontal position on the fived circular surface of radius R=0. 11mL 2 /12. A horizontal force P of magnitude 75 N is applied at end B. a. ) Mechanical Engineering. 143g down slot. 0 kg is free to rotate on a frictionless pin. The uniform slender rod of mass m and length L is released from rest in the inverted vertical position shown. 5mL 2 /12. The uniform slender rod of mass m and length l is hinged at A and is attached to the four linear springs and one torsional spring as shown. A horizontal force P = 75 N is applied at the end B. Question 3: A uniform slender rod of mass m and length L is hinged at point o, and is attached to four linear springs and one torsional spring, as shown in this Figure. A uniform slender rod of length L = 1140 mm and mass m= 5. Knowing that the coefficients of friction are =0. 2 m above 0. Evaluate your result for theta = 20 degree, L = 465 mm, and m = 6. 5 lb is applied at B horizontally to the left at h, determine (a) the distance h for which the horizontal component of the reaction at A is zero, (b)the corresponding angular acceleration of the rod. Determine the value of w which will result in a zero moment supported by the weld at A for the position 8 = 60° with b = 1/4. A slender, uniform metal rod of mass M and length l is pivoted without friction about an axis through its midpoint and perpendicular to the rod. (©) Determine for the Here’s the best way to solve it. Assuming perfectly elastic impact at both A and B. A uniform slender rod of length L = 36 inches. Q. (Round the final answer to one decimal place. Evaluate your result for θ=30∘. 078. Determine the angular acceleration of the rod. 3 m and point A is initially h = 0. If a force P of magnitude 1. 5m Mass:m 2L Length:L b) Solve the same A A uniform slender rod of length L=900 mm and mass m=4 kg is suspended from a hinge at C. 6 lb hangs freely from a hinge at AA force P of magnitude 1. Solution 218. C. l = 3F (2L 3) AY + 2F (L 3) AY. B: If the initial conditions are θ (0) = θ o, θdot (0) = w o, find the total solution for θ (t). 5 lb is applied at B horizontally to the left (h = L), determine (a) the angular acceleration of the rod, (b) the components of the reaction at A. Question: The uniform slender rod of mass m and length L is released from rest in the inverted vertical position shown. 100% (7 ratings) A uniform slender rod of length = 42 in, and weight W= 4. a - Rotation about a flxed point: Equations of motion: Angular acceleration Determine the angular acceleration of the rod. Determine the tension in cable A immediately after cutting cable B. Given that Mass =M L …. The 4-kg uniform slender bar BD is attached to bar AB and a wheel of negligible mass that rolls on a circular surface. Problem statement: A uniform slender rod of mass m and length l is hinged at point A and is attached to four linear springs and one torsional spring, as shown in Fig. Knowing that at the instant shown bar AB has an angular velocity of 6 rad/s and no angular acceleration, determine the reaction at point D. P3. A uniform slender rod of length L = 1260 mm and mass m= 5. (b) Show that any line passing through O is a principle axis. A P B Problem 16. b - Angular acceleration Determine the corresponding angular acceleration of the rod. 5 lb is applied at Bhorizontally to the left (n=1). A horizontal force P of magnitude 75 N is applied at end 8. customers who used Chegg Study or Chegg Study Pack in Q2 2023 and Q3 2023. A 21 -lb uniform slender rod AB of length L= 32-in is riveted to a 16-lb uniform disk of radius, R= 8-in and pinned at B as shown. The force components of the reactions at point C. Three uniform slender rods of mass M and length L each are rigidly attached to each other to form a mutually orthogonal frame as shown in the figure on the right (a) Find the moment of inertia of the frame for the line passing through P and Q. (Round the final answer to two decimal places. A uniform slender rod of length L = 36 in. ) b. 0 m and mass M=2. 9 kg. l = 8F L 3AY. Since support B is slightly lower than support A, the rod strikes A with a velocity Vi before it strikes B. is held in equilibrium as shown, with one end against a frictionless wall and the other end attached to a cord of length S 30 in. What is the mass moment of inertia of the frame about the axis directed perpendicular to the diagram and passing through point O? A. Suppose you have a uniform cube of mass m with edges of Expert-verified. Find the tension in the cable at B at the instant the other cable at A ruptures suddenly. 5-6 One end of a uniform slender rod of mass m and length / slides along a frictionless vertical surface while the other end of the rod slides along a frictionless horizontal surface as shown in Fig. А P B Determine the distance for which the horizontal component of the reaction at C is zero. ) The motion of the uniform slender rod of length L=0. B. A: Fig. Note that it will not be necessary to explicitly find keq A uniform slender rod of length L = 1020 mm and mass m = 4. ) Determine the natural (angular) frequency of the. A horizontal force P=75 N is applied at end B. Use the results of Example 9. Oct 27, 2004 · A uniform slender rod of length l and mass m is secured to a circular hoop of radius l as shown. 76 A uniform slender rod of length L=36 in. Since support B is slightly lower than support 4, the rod strikes A with a velocity vi before it strikes B (see Fig. Similar questions. Neglect friction and the mass of the small end roller and find the initial acceleration of A Evaluate your result for theta = 30 degree. aA=1. Dec 2, 2022 · A uniform slender rod of mass \( m \) and length \( L \) is released from rest, with its lower end touching a frictionless horizontal floor. 285 mm. Introduction:- A measurement of an object's resistance to rotational changes is called the moment of Part A Suppose a uniform slender rod has length L and mass m. 310 Problem 218. Assume that the rod has mass m and length of L. Knowing that a horizontal force P of magnitude 75 N is applied at end B, determine (a) the distance r for which the horizontal component of the reaction at C is zero. The rod reaches state 2 at 6 = 45° and then reaches state 3 at 0 = 0°. 24–Oct 12, 2023 among a random sample of U. Since the total length L has mass M, then M/L is the proportion of mass to length and the mass element can be expressed as shown. 8, determine the angular velocity of the Get four FREE subscriptions included with Chegg Study or Chegg Study Pack, and keep your school days running smoothly. A uniform slender rod of length L and cross sectional area A is rotating in a horizontal plane about a vertical axis through one end. (c) again 16. Find the moment of inertia through the end of the rod. Know that 7- 275 mm. A horizontal spring, assumed massless and with force constant k, is attached to the lower end of the rod, with the other end of the spring attached to a rigid support. 4 kg is suspended from a hinge at C. A force P of magnitude 1. If the rod and hoop are released from rest on a horizontal surface in the position illustrated, determine the initial values of the friction force F and normal force N under the hoop if friction is sufficient to prevent slipping. 10. Knowing that at the instant shown the rod has an angular velocity of 3 rad/s counterclockwise and theta= 30 degrees, determine reactions at point A and The uniform slender rod has a mass m. 78 A uniform slender rod of length L = 900 mm and mass m = 4 kg is suspended from a hinge at C. Determine the distance 7 for which the horizontal component of the reaction at C is zero. Respondent base (n=611) among approximately 837K invites. 10 to find the mass moments of inertia about the xyz axes passing through the center of mass G. If the rod and hoop are released from rest on a horizontal surface in the position illustrated, determine the initial values of the . 4. 5 m is released from rest in the horizontal position illustrated, where x = 0. A frame is made of two uniform slender rods each with the same mass m and length L. 100% (28 ratings) Step 1. Find the natural frequency of the system. Question: NOTE: This is a multi-part question. Answer: μ1= The uniform slender rod of length l = 230 mm is released from rest in the dashed vertical position. Find the natural frequency of the system if k = 2000 N/m, k = 1000 N-m/rad, m = 10 kg, and ! = 5 m. A belt is attached to the rim of the disk and then to a spring with spring constant, k= 25-lb/in which holds the rod/disk at rest in the equilibrium position shown. The rod is released from rest at state 1 (0 = 90°). A uniform slender rod of length L = 900 mm is suspended from a hinge at C. P1 consists of a uniform slender rod of mass m and length l. kh ux mh pb py hk vr mh ab ht