PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 20, Problem 50P
To determine
The velocity of package
The acceleration of package
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The two V-belt pulleys form an integral unit
and rotate about the fixed axis at O. At a
certain instant, point A on the belt of the
smaller pulley with a distance of DA = 143
mm has a velocity VA = 2.8 m/s, and point B
on the belt of the larger pulley with a
distance of DB = 900 mm has an acceleration
ag = 43 m/s? as shown. For this instant
determine the magnitude of the acceleration
ac of point C in m/s? if Rc = 374 mm.
ав
В
DB
UA
Rc
A
DA
The boom OAB pivots about point O, while section AB simultaneously extends from within section OA. Determine the velocity and
acceleration of the center B of the pulley for the following conditions: 0 = 26°, 0 = 7 deg/sec, 0 = 2 deg/sec², 1 = 10 ft, 1 = 1.0 ft/sec, ï =
-5.9 ft/sec². The quantities and I are the first and second time derivatives, respectively, of the length / of section AB. Express your
answers as vectors in the e, and en directions.
+1
B
26'
A
eo) ft/sec
eg) ft/sec²
Answers:
VB =
(
aB =
i
8
2
er +
i
e₁+ i
The boom OAB pivots about point O, while section AB simultaneously extends from within section OA. Determine the velocity and
acceleration of the center B of the pulley for the following conditions: 0 = 30°, 0 = 7 deg/sec, 0 = 8 deg/sec², 1 = 7 ft, 1 = 2.2 ft/sec, Ï =
-2.3 ft/sec². The quantities and I are the first and second time derivatives, respectively, of the length / of section AB. Express your
answers as vectors in the e, and en directions.
0
Answers:
VB =
ав =
(i
26'
8
A
O
er +
er +
B
eo) ft/sec
eo) ft/sec²
Chapter 20 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
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 boom OAB pivots about point O, while section AB simultaneously extends from within section OA. Determine the velocity and acceleration of the center B of the pulley for the following conditions: 0 = 29°, O = 3 deg/sec, Ö = 7 deg/sec?, 1 = 15 ft, İ = 2.6 ft/sec, i = 2.4 ft/sec2. The quantities l and l are the first and second time derivatives, respectively, of the length I of section AB. Express your answers as vectors in the e, and eg directions. B 27' Answers: VB = i ee) ft/sec ag = i eg) ft/sec?arrow_forwardThe cars on the amusement-park ride rotate around the axle at A with a constant angular velocity wa/f = 2 rad/s, measured relative to the frame AB. At the same time the frame rotates around the main axle support at B with a constant angular velocity wf = 1 rad/s. Determine the velocity and acceleration of the passenger at C at the instant shown. D 8 ft- WA/f = 2 rad/s/ 8 ft 15 ft wf = 1 rad/s O)B Xarrow_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_forward
- The member OA of the industrial robot telescopes and pivots about the fixed axis at point O. At the instant shown, 6 = 60°, 6 = 1.2 rad/s, 6 =0.8 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 about a vertical axis. 1.1 m 0.9 m 15°arrow_forwardThe boom OAB pivots about point O, while section AB simultaneously extends from within section OA. Determine the velocity and acceleration of the center B of the pulley for the following conditions: 0 = 30°, 0 = 5 deg/sec, Ö = 5 deg/sec², l = 14 ft, 1 = 1.8 ft/sec, i = -2.5 ft/sec?. The quantities l and i are the first and second time derivatives, respectively, of the length l of section AB. Express your answers as vectors in the e, and eg directions. 21' Answers: VR = (i е, + i eg) ft/sec ag = (i е, + i eg) ft/sec2arrow_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
- 4. As shown in the image below, the bucket of the backhoe traces the path of the cardioid r = C · (1 – cos 0) ft, where constant C= 28. At this instant angle 0 - = 121°, and the boom is rotating with an angular velocity of 0 = 2.3 rad/s and an angular acceleration of 0 = 0.19 rad/s?. Determine the magnitude of the acceleration of the bucket in rad/s². Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Your Answer: Answerarrow_forwardAt the instant shown, the arm OA of the conveyor belt is rotating about the Z axis with a constant angular velocity w₁ = 6.5 rad/s, while at the same instant the arm is rotating upward at a constant rate w₂ = 3.6 rad/s. (Figure 1) Figure 7=6ft 10-450 Part A If the conveyor is running at a rate=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 I, y, and 2 components of the velocity in feeet per second to three significant figures separated by commas. IVE] ΑΣΦΩΤΟ Vp = Submit Part B ap= Request Answer Submit Determine the acceleration of the package P at the instant shown. Enter the I, y, and 2 components of the acceleration in feet per second squared to three significant figures separated by commas. ΠΙΑΣΦΩΠ Request Answer vec 6 A < Return to Assignment vec ? Provide Feedback ft/s ? ft/s²arrow_forwardConsider the portion of an excavator shown. At the instant under consideration, the hydraulic cylinder is extending at a rate of 5 in./sec, which is decreasing at the rate of 2 in./sec every second. Simultaneously, the cylinder is rotating about a horizontal axis through O at a constant rate of 13 deg/sec. Determine the velocity v and acceleration a of the clevis attachment at B. Write the velocity and acceleration as vectors.Answers:v = ( er + eθ) in./seca = ( er + eθ) in./sec2arrow_forward
- Consider the portion of an excavator shown. At the instant under consideration, the hydraulic cylinder is extending at a rate of 6 in./sec, which is decreasing at the rate of 2 in./sec every second. Simultaneously, the cylinder is rotating about a horizontal axis through O at a constant rate of 14 deg/sec. Determine the velocity v and acceleration a of the clevis attachment at B. Answers: v=i a = ( 3.7' 38⁰ 2.8' A i e, + i B eg) in./sec ee) in./sec²arrow_forward2. A car is traveling along the circular curve of radius r = 90 m. At the instant shown, its angular rate of rotation is 0 = 0.4 rad/s, which is increasing at the rate of 0 = 0.2 rad/s² . Determine the magnitude of the car's velocity and acceleration at this instant. A r = 300 ft è = 0.4 rad/s Ö = 0.2 rad/s2arrow_forwardThe boom OAB pivots about point O, while section AB simultaneously extends from within section OA. Determine the velocity and acceleration of the center B of the pulley for the following conditions: 0 = 16°, 0 = 2 deg/sec, Ô = 7 deg/sec?,1 = 11 ft, 1 = 2.1 ft/sec, i = -3.9 ft/sec?. The quantities i and i are the first and second time derivatives, respectively, of the length I of section AB. Express your answers as vectors in the e, and ee directions. B 28' A Answers: VB = ( i %3D e, + eə) ft/sec ав (i e, + eg) ft/sec2arrow_forward
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