Planar Rigid Body Kinematics Homework

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1 Chapter 2: Planar Rigid ody Kinematics Homework Chapter 2 Planar Rigid ody Kinematics Homework Freeform c

2 Chapter 2: Planar Rigid ody Kinematics Homework 2-2 Freeform c 2018

3 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2. Given: square plate (having side lengths of = 2 m) rotates with a counterclockwise sense at a rate of Ω = 5 rad/s aout a shaft passing through corner. t the position shown elow, corner is directly aove the shaft. Find: Consider the following two parts of this prolem: (a) For the first part, we are given that the rotation rate of the plate is changing at a rate of Ω = 10 rad/s 2. Determine the velocity and acceleration vectors for corners and of the plate. Make sketches of these vectors. () For the second part, we are not given information on Ω. Instead, we know the acceleration of corner to e in the negative y-direction (the x-component is zero), as shown in the figure elow. For this, determine the numerical value of Ω and of the acceleration vector for corner. Make a sketch of the acceleration vector for corner. y y Ω Ω! a x x Part (a) Part () Freeform c

4 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2. Given: disk, having an outer radius of R, rotates with a rate of Ω aout a shaft passing through its center, with Ω increasing at a rate of Ω. The shaft is supported y a pair of earings on cart. Cart is moving to the right with a speed of v and an acceleration of a. t the instant of interest, point on the perimeter of the disk is at the same height as. Find: For this prolem: (a) Determine the velocity of point. Write your answer as a vector in terms of its xyz components. () Determine the acceleration of point. Write your answer as a vector in terms of its xyz components. y y R Ω z R x Ω v,a SIDE view RIGHT END view of disk 2-4 Freeform c 2018

5 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2.C Given: Rigid ody is shaped as quarter-circle arc with a radius of R. End of the ar is constrained to move along a vertical wall, whereas end moves along an incline at an angle of θ = with respect to the horizontal. t the instant shown, the center of the arc is directly elow end, and end moves with a constant speed of v. Find: For this prolem: (a) Determine the velocity and acceleration of end of the ar. Express your answers as vectors and in terms of the parameters of v and R. () Is the speed of increasing, decreasing or constant? R v θ Freeform c

6 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2.D Given: Roller D of the mechanism shown is moving downward along a straight vertical surface with a constant speed of v D. t the instant shown, link is vertical. Find: For this position: (a) Determine the angular velocities of links and D. Write your answers as vectors. () Determine the angular accelerations of links and D. Write your answers as vectors. D L! v D 2L Use the following parameters in your analysis: θ = 53.13, L = 2 m and v D = 15 m/s. 2-6 Freeform c 2018

7 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2.E Given: The compound wheel assemly shown elow is driven y a cale attached to the outer rim of the assemly at point. The wheel rolls without slip at point with point C moving to the right with a speed of v C, and the acceleration at point is given y a = a x î + a y ĵ Find: Determine the acceleration of the center point C of the pulley. φ y R r x no slip C v C Use the following parameters in your analysis: R = 0.1 m, r = m, φ = 0, a x = 8 m/s 2 and a y = -3 m/s 2. Freeform c

8 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2.F Given: The circular disk shown rolls without slipping on a straight horizontal surface. ar is pinned to point on the disk, with end constrained to move along a smooth horizontal surface with a constant speed v. t the position shown, is directly to the right of the center of the disk. Find: For this position: (a) Determine the angular velocities of link and of the disk. Write your answers as vectors. () Determine the angular accelerations of link and of the disk. Write your answers as vectors. no slip R L v C Use the following parameters in your analysis: R = 6 in, L = 10 in and v = 100 in/s. 2-8 Freeform c 2018

9 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2.G Given: The mechanism shown is made up of rigid links, and CD. Link has a pin joint at end and is known to e rotating in the clockwise sense aout with a rotation rate of ω. is pinned to at end and is pinned to a slider at, with moving along a horizontal guide. Link CD connects the center C of to a second slider at D through pin joints, with this slider constrained to move along a vertical guide. t the instant shown link is oriented vertically, is directly elow D and D is directly to the right of. Find: For this prolem: (a) Locate the instant center (IC) for link. ased on the location of this IC, what is the speed of pin C and the direction of travel for C, as well as the speed of slider? () Locate the IC for link CD. ased on this location, determine the speed of slider D. NTE: Please use only the instant center approach for this prolem. Do not use vector analysis to find your answers. D 0.6L 0.5L C ω 0.5L Freeform c

10 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2.H This prolem has three parts. In each part, you are asked to use the instant center approach in answering the questions related to the prolems. In all cases, the figures are drawn to scale. Please use a straight edge when making your drawings. PRT In the mechanisms shown elow, link is rotating in the counterclockwise sense. For the position shown of ECH mechanism: (a) Determine the location of the instant center for link. () Determine the directions of rotation for links and D. Justify your answers in words. (c) Which is larger: ω or ω? Justify your answers in words. ω ω D D 2-10 Freeform c 2018

11 Chapter 2: Planar Rigid ody Kinematics Homework PRT In the mechanism shown elow, link is rotating in the counterclockwise sense. (a) Determine the locations of the instant centers for links, E and EG. () Determine the directions of rotation for links, E and EG. Justify your answers in words. D G ω E slider F Freeform c

12 Chapter 2: Planar Rigid ody Kinematics Homework PRT C Link, having a length of L = 5 in, is part of a planar mechanism. t the instant shown, the velocities of points and are known to e oth perpendicular to a line connecting and, with v = 3v = 30 in/s. Determine the location of the instant center for link. v L v 2-12 Freeform c 2018

13 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2.I Given: mechanism is made up of rigid links,, C and DE. slider is pinned to end E of link DE and is constrained to move along a horizontal guide. For the position shown, link is rotating in the counterclockwise sense aout with a constant rotation rate of ω, with links and C eing vertically oriented and link eing horizontally oriented. Find: For the position shown: (a) Use the instant center approach to determine the angular velocities of links, C and DE, along with the speed of slider E. () Use vector analysis to determine the angular accelerations of links, C and DE, along with the acceleration of slider E. Is the speed of E increasing, decreasing or constant at this instant? ω L 2L L L D 3L E C Freeform c

14 Chapter 2: Planar Rigid ody Kinematics Homework Homework H.2.J Given: mechanism is made up of lock, a circular disk having an outer radius of R and link D. lock is constrained to move along a horizontal surface with the disk eing ale to roll without slipping on lock. Link D is pinned to point on the disk and to a slider at D, with the slider eing constrained to move along a horizontal guide. t the instant shown, is directly to the right of the center C of the disk, and lock moves to the left with a constant speed of v. Find: For the position shown: (a) Determine the angular velocities of the disk and link D. Write your answers as vectors. () Determine the angular accelerations of the disk and link D. Write your answers as vectors. v R C R 2 no slip 5R / 3 D 2-14 Freeform c 2018

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