EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137616909
Author: HIBBELER
Publisher: VST
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Chapter 20, Problem 43P
To determine
The velocity of point
The acceleration of point
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End A of the 3.6-ft link has a velocity of 3.7 ft sec in the direction shown. At the same instant, end B has a velocity whose magnitude is
4.4 ft/sec as indicated. Find the angular velocity w of the link in two ways. The angular velocity of the link is positive if
counterclockwise, negative if clockwise.
A
VA = 3.7 ft/sec
40°
Answer: w=
3.6'
B
B
VB = 4.4 ft/sec
rad/sec
At the instant shown, the tower crane rotates about the z axis with an angular velocity ω1=0.25rad/s, which is increasing at 0.6 rad/s2. The boom OA rotates downward with an angular velocityω2=0.4 rad/s, which is increasing at 0.8 rad/s2. Determine,the
Velocity
Accelerationof point A located at the end of the boom at this instant.
The
two rotor blades of 770-mm radius rotate about the shaft at O mounted in the sliding block. The acceleration of the block
ao = 5.2 m/s². If Ò = 0 and 0 = 4.2 rad/s² when 0 = 0, find the magnitude of the acceleration of the tip A of the blade for this
instant.
770
A
mm
ao
Chapter 20 Solutions
EBK ENGINEERING MECHANICS
Ch. 20 - The propeller of an airplane is rotating at a...Ch. 20 - The disk rotates about the z axis at a constant...Ch. 20 - The ladder of the fire truck rotates around the z...Ch. 20 - The ladder of the fire truck rotates around the z...Ch. 20 - At a given instant, the antenna has an angular...Ch. 20 - The disk rotates about the shaft S, while the...Ch. 20 - The electric fan is mounted on a swivel support...Ch. 20 - The electric fan is mounted on a swivel support...Ch. 20 - The truncated double cone rotates about the z axis...Ch. 20 - Prob. 20P
Ch. 20 - Gear B is driven by a motor mounted on turntable...Ch. 20 - Prob. 22PCh. 20 - Prob. 23PCh. 20 - Prob. 26PCh. 20 - Prob. 27PCh. 20 - Prob. 30PCh. 20 - So1ve Example 20.5 such that the x, y, z axes move...Ch. 20 - Prob. 38PCh. 20 - At the instant = 60, the telescopic boom AB of...Ch. 20 - Prob. 40PCh. 20 - Prob. 42PCh. 20 - Prob. 43PCh. 20 - Prob. 44PCh. 20 - Prob. 46PCh. 20 - Prob. 47PCh. 20 - Prob. 48PCh. 20 - Prob. 49PCh. 20 - Prob. 50PCh. 20 - Prob. 51P
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- The disk rotates with the angular motion shown. Determine the angular velocity and angular acceleration of the slotted link AC at this instant. The peg at B is fixed to the disk. w = 6 rad/s a = 10 rad/s² A 30° 0.3 m 0.75 m 30° Barrow_forwardFor a short time the bucket of the backhoe traces the path of the cardioid r=25(1−cosθ)ft. The boom is rotating with an angular velocity of θ˙omega = 2.3 rad/s and an angular acceleration of θ¨alpha = 0.16 rad/s^2 at the instant shown 1)Determine the magnitude of the velocity of the bucket when θ = 120∘ 2)Determine the magnitude of the acceleration of the bucket when θ = 120∘arrow_forwardAt the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity w 6.5 rad/s, while at the same instant the arm is rotating upward at a constant rate w₂=3.9 rad/s (Figure 1) Figure 0-45° ▼ Part A If the conveyor is running at a rate r = 5 ft/s, which is increasing at F-8 ft/s². determine the velocity of the package Pat the instant shown. Neglect the size of the package. Enter the z, y, and z components of the velocity in feeet per second to three significant figures separated by commas. vp Part B Submit LVE| ΑΣΦ | 11 ap vec Submit Request Answer Determine the acceleration of the package P at the instant shown Enter the z, y, and a components of the acceleration in feet per second squared to three significant figures separated by commas. IVE] ΑΣΦ | 11 vec 52 C Request Answer ft/s ? ft/s²arrow_forward
- At the instant θ = 60∘, link CD has an angular velocity ωCD = 4 rad/s and an angular acceleration αCD = 3 rad/s2. The collar at C is pin connected to DC and slides over B as shown in (Figure 1). A) Determine the magnitude of the angular velocity of rod AB at this instant. B) Determine the magnitude of the angular acceleration of rod AB at this instant.arrow_forwardThe two rotor blades of 770-mm radius rotate about the shaft at O mounted in the sliding block. The acceleration of the block is aO = 5.2 m/s2. If θ˙θ˙ = 0 and θ¨θ¨ = 4.2 rad/s2 when θ = 0, find the magnitude of the acceleration of the tip A of the blade for this instant..arrow_forward2. The angular velocity of the drum is increased uniformly from 6 rad/s when t = 0 to 10 rad/s when t = 4 s. Find the magnitudes of the velocity and acceleration of points A and B on the belt the instant when t = 3 s. 4 in.arrow_forward
- Bar AB is pinned to the fixed support at A, and the collar B is pinned to the bar at its opposite end. The bar CD can slide freely through the collar at B. At the instant shown, bar AB is horizontal, /= 1.2 m, s = 1.07 m, 0 = 60°, and wAB= 40 rad/s. If ªäß = 21 rad/s² at the instant shown, determine the angular velocity and angular acceleration of the bar CD. WAB αAB с. B The angular velocity of the bar CD is The angular acceleration of the bar CD is k rad/s. k rad/s².arrow_forwardAt the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity w₁ = 5.6 rad/s, while at the same instant the arm is rotating upward at a constant rate w2 = 4.4 rad/s. (Figure 1) Figure 0₁ r = 6 ft 10=45° A 1 of 1 Part A If the conveyor is running at a constant rate r = 5 ft/s, determine the velocity of the package P at the instant shown. Neglect the size of the package. Enter the x, y, and z components of the velocity in feet per second to three significant figures separated by commas. ΠΑΣΦ11 vp = Submit Part B ap = Request Answer Submit Determine the acceleration of the package P at the instant shown. Enter the x, y, and z components of the acceleration in feet per second squared to three significant figures separated by commas. IVE ΑΣΦ1 Request Answer vec < Return to Assignment vec ? Provide Feedback ft/s ? ft/s²arrow_forwardAn external drive system actuates the mechanism by applying a moment M at bearing D. At the instant 0 = 25°, the magnitude of the velocity vector of point C is 20 m and the angular acceleration of link CD is 45 rad in the CCW direction. s2 rad Determine the angular acceleration vector of link CE (in ) at this instant. Consider L = 6 metres. E 2 4 Marrow_forward
- The disk rotates about the shaft S, while the shaft is turning about the z axis at a rate of ωz = 5.5 rad/s , which is increasing at α = 2.5 rad/s2 . No slipping occurs. Determine the x, y, and z components of the velocity of point B on the disk at the instant shown using scalar notation. Determine the x, y, and z components of the acceleration of point B on the disk at the instant shown using scalar notation.arrow_forwardThe member OA of the industrial robot telescopes and pivots about the fixed axis at point O. At the instant shown, 0 = 60°, 6 = 1.2 rad/s, 60.8 rad/s2, OA = 0.9 m, OA 0.5 m/s, and OA = -6 m/s2. Determine the magnitudes of the velocity and acceleration of joint A of the robot. Also, sketch the velocity and acceleration of A and determine the angles which these vectors make with the posi- tive x-axis. The base of the robot does not revolve %3D about a vertical axis. 1.1 m. 0.9 m 15° Parrow_forwardAt the instant shown, the shaft and plate rotates with an angular velocity of 19 rad/s and angular acceleration of 9 rad/s². (Figure 1) Figure X D 0.4 m B 0 0.4 m a 0.3 m < 1 of 1 0.6 m 0.2 m C 0.3 m Part A Determine the velocity of point D located on the corner of the plate at this instant. Enter the x, y, and z components of the velocity in meters per second to three significant figures separated by commas. ► View Available Hint(s) (UD), (UD)y, (UD) z = 6.51,4.89,1.63 m/s Submit Previous Answers ✓ Correct Here we learn how to determine the velocity of a point on a rigid body revolving with an angular acceleration about a fixed axis in three dimensions. Part B Determine the acceleration of point D located on the corner of the plate at this instant. Enter the x, y, and z components of the acceleration in meters per second squared to three significant figures separated by commas. ► View Available Hint(s) (ap)z, (ap)y, (ap)₂ = [Π ΑΣΦ | ↓↑ vec Submit Previous Answers X Incorrect; Try…arrow_forward
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