### Problem StatementAt the instant shown, the disk is rotating with an angular velocity of \( \omega = 2 \, \text{rad/s} \) and has an angular acceleration of \( a = 1 \, \text{rad/s}^2 \). Determine the velocity and acceleration of cylinder \( B \) at \( \Theta = 45^\circ \).Neglect the size of the pulley at \( C \), use the Relative motion method.### Diagram ExplanationThe diagram shows a mechanical setup with a rotating disk, labeled \( A \), that has:- A marked center point \( O \) around which the disk rotates.- An angular velocity vector \( \omega \) indicating the rotational speed and direction.- An angular acceleration \( a \) indicating the change in angular velocity.A rod extending from point \( A \) to point \( C \) connects the disk to a pulley. The distance from the center \( O \) of the disk to point \( A \) is 3 ft, and from \( A \) to \( C \) is 5 ft. Cylinder \( B \) is connected to the pulley at \( C \) by a cable.### InstructionsThe task is to use the Relative motion method to find the velocity and acceleration of cylinder \( B \), given the initial conditions and the specific angle \( \Theta = 45^\circ \).

Given: The radius of the disk, r = 3 ft The angular velocity of the disk, w = 2 rad/s The angular acceleration of the disk, α = 1 rad/s² The position, θ = 45ᵒThe angle tends by AC with horizontal, α = tan-1[3sin45/(5-3cos45)] = 36.386ᵒ The length of AC, ACcos36.383 = 5 - 3cos45 AC = 3.575 ft The velocity of the point A, V₁ = vo + rw = 0 + [3cos45i + 3sin45j][2k] = 4.242i + 4.242k …. (1) The velocity of the point C with respect to the point A, V₂ = v₁ + rw = 4.242i + 4.242k + [-3.575cos36.386i + 3.575sin36.386j][w′k] = [2.1207w′ + 4.242]i + [4.242 – 2.878w′]j ……(2) The velocity of C with respect to B, V₂ = -v₃j …….(3) From equation (2) and (3), 2.1207w′ + 4.242 = 0 w′ = -2 rad/s and 4.242 – 2.878w′ = -v₃ v₃ = -4.242 + 2.878[2] = 1.514 ft/s …...AnswerThe acceleration of A with respect to disk center, a₁ = ao + rα + rw² = 0 + [3cos45i + 3sin45j] [1k] + [3cos45i + 3sin45j][2k]² = 6.3639i + 10.606j …..(3) The acceleration of C with respect A, a₂ = a₁ + AC[αAC] + AC[w′]² = 6.3639i + 10.606j + [-3.575cos36.386i + 3.575sin36.386j] [αAC k] + [-3.575cos36.386i + 3.575sin36.386j][-2k]² = [-5.148 + 2.127 αAC ]i + [19.077 + 2.878 αAC ]jj …… (4) The acceleration of C with respect to B, a₂ = -a₃j …. (5) On comparing equation (5) and (4), [-5.148 + 2.127 αAC ] = 0 αAC = 2.42 rad/s² -a₃ = [19.077 + 2.878 αAC ] = 19.077 + 2.878x2.42 a₃ = -26.041 ft/s² ………Answer

Engineering

Mechanical Engineering

At the instant shown, the disk is rotating with an angular velocity of w = 2 rad/s and has an angular acceleration of a = 1 rad/s2. Determine the velocity and acceleration of cylinder B at Ⓒ = 45° Neglect the size of the pulley at C, use Relative motion method. 3 ft 5 ft B

At the instant shown, the disk is rotating with an angular velocity of w = 2 rad/s and has an angular acceleration of a = 1 rad/s2. Determine the velocity and acceleration of cylinder B at Ⓒ = 45° Neglect the size of the pulley at C, use Relative motion method. 3 ft 5 ft B

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: e DC bar of the connection rotates with an angular velocity of 3 rad/s d an angular acceleration of…

Q: At the instant shown, the arm AB is rotating about the fixed pin A with an angular velocity w₁ = 4.6…

A: The angular velocity of AB is The angular acceleration of AB is The angular velocity of BD relative…

Q: The disk is originally rotating at 8 rad/s. If it is subjected to constant angular acceleration of 6…

A: wo = 8 rad/s alpha = 6 rad/s^2 V=? Answer: 22.0000 ft/s2

Q: At the instant shown, the disk is rotating with an angular velocity of w = 2 rad/s and has an…

Q: At the instant when 0 = 60°, the slotted guide rod is moving to the left with an acceleration of 2…

Q: At a given instant the wheel of radius r = 0.8 m is rotating with angular velocity w = 3 rad/s and…

Q: The pinball machine paddle, P, pushes the pinball which weighs 0.7 N along the slot shown. This…

Q: The disk rotates about a fixed axis through point O with a clockwise angular velocity wo - 17 rad/s…

A: Concept Of Sine Law Is Used

Q: The disk rotates about a fixed axis through point O with a clockwise angular velocity wo = 17 rad/s…

A: ωO=17 rad/sαO=5.1 rad/s2r=250mm To Find: vrel, αrel, ωBC,αBC

Q: The pinball machine paddle P pushes the pinball which has a mass of 150 g along the slot shown. This…

A: Given:The mass of the pinball, The angular velocity of the paddle, The value of distance, The value…

Q: The boom OAB pivots about point O, while section AB simultaneously extends from within section OA.…

Q: At the instant shown, link CD rotates with an angular velocity of W = 7.5 rad/s. If it is subjected…

Q: The disk has an angular acceleration a =8 rad.s2 and an angular velocity w =2rad.s1 at the instant…

A: Given That r=0.5mα=8rad/s2ω=2rad/s

Q: At the instant = 29°, crank AB rotates with an angular velocity of 10 rad/s and an angular…

A: Given information:Angular velocity of crank AB, ω=10rad/sAngular acceleration of crank AB,…

Q: When the mechanism is in the position shown, the velocity of the sliding collar is VA = 1.6 m/s, and…

A: Data given-

Q: 3. In the mechanism shown collar B slides with a constant speed up = 1 ft/sec to the right on the…

A: The dimension are The velocity of point B is constant

Q: Point A of the circular disk is at the angular position 0 = 0 at time t = 0. The disk has angular…

Q: Link AB has the angular velocity of 2 rad/s and angular acceleration of 6 rad/s². Determine the…

Q: For For clockwise. the instant when = B = 60°, the hydraulic cylinder gives A a velocity VA = 5.9…

Q: At the instant shown, the lower rack is moving to the right with a speed of v₁ = 4.2 ft/s, while the…

A: thank you

Q: Member AB has the angular motions shown. Determine the velocity of slider C, the angular velocity of…

A: To Find-The velocity of slider C, The angular velocity of member BC, The acceleration of slider C,…

Q: wn has the roller A ft/s with an acceleration etermine the angular 10 ft B and also the linear int G…

Q: At the instant shown, bar AB is rotating at 15 rad/s in the counterclockwise direction and has a…

Q: The disk is moving to the left such that it has angular acceleration α and angular velocity ω at the…

A: Step 1:Angular acceleration is 8s2radAngular speed is3sradAngle ϕ is45oAngle θ is30oRadius is…

Q: Write the vector expression for the acceleration a of the mass center G of the simple pendulum in…

Q: The disk has an angular acceleration a =7 rad.s2 and an angular velocity w =1rad.s 1 at the instant…

A: Calculated acceleration at point B.

Q: The boom OAB pivots about point O, while section AB simultaneously extends from within section OA.…

A: The value are

Q: Determine the angular acceleration() of the 100kg slender rod at the instant shown. The bar has 0…

A: Given,

Q: At the instant represented, the velocity of point A of the 1.2m bar is 3 m/s to the right. Determine…

Q: The two rotor blades of 770-mm radius rotate about the shaft at O mounted in the sliding block. The…

Q: The cars on the amusement-park ride rotate around the axle at A with a constant angular velocity…

A: The angular velocity frame is .The angular velocity of axle is .

Q: A D в Bar AC rotates at wAĆ 3 k- rad with an angular acceleration of a AC rad 1.4 k At that instant,…

A: given : ωac= 3k^ rad/sec αac→ = 1.4k^ rad/sec2 ϕ = 55° θ…

Q: An external drive system actuates the mechanism by applying a moment M at bearing D. At the instant…

A: Given: Angle, θ=30 Velocity of C, νc=16 m/s Angular acceleration of C, αc=40 rad/s2 To find : X -…

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Problem Statement

At the instant shown, the disk is rotating with an angular velocity of \( \omega = 2 \, \text{rad/s} \) and has an angular acceleration of \( a = 1 \, \text{rad/s}^2 \). Determine the velocity and acceleration of cylinder \( B \) at \( \Theta = 45^\circ \).

Neglect the size of the pulley at \( C \), use the Relative motion method.

### Diagram Explanation

The diagram shows a mechanical setup with a rotating disk, labeled \( A \), that has:

- A marked center point \( O \) around which the disk rotates.
- An angular velocity vector \( \omega \) indicating the rotational speed and direction.
- An angular acceleration \( a \) indicating the change in angular velocity.

A rod extending from point \( A \) to point \( C \) connects the disk to a pulley. The distance from the center \( O \) of the disk to point \( A \) is 3 ft, and from \( A \) to \( C \) is 5 ft. Cylinder \( B \) is connected to the pulley at \( C \) by a cable.

### Instructions

The task is to use the Relative motion method to find the velocity and acceleration of cylinder \( B \), given the initial conditions and the specific angle \( \Theta = 45^\circ \).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

REN 5.2.2/3 The hoop is cast on the rough surface such that it has an angular velocity = 3 rad/s and an angular acceleration a = 8 rad/s². Also, its center has a velocity of v.= -51 m/s and a deceleration a 21 m/s². Determine the acceleration of point B at this instant. DIS 12 ~15 D f Nº 0.39 an=r w² an= 0.s. 32 an = 43 an B 30° 0.5 m w = 3 rad/s x = 8 rad/s² D
At the instant 8 = 32°, crank AB rotates with an angular velocity of 9 rad/s and an angular acceleration of 3 rad/s². Determine the acceleration of the slider block C at this instant. Take a=b=0.4 m. B
The hydraulic cylinder imparts a constant upward velocity v_A = 0.25 m/s to corner A of the rectangular container during an interval of its motion. For the instant when theta = 16 degree, determine the velocity v_B and acceleration a_B of roller B. Also, determine the corresponding angular velocity co of edge CD
A disk oscillates about its axis of rotation given by its angular acceleration of ∝ = -kθ. First determine the value of k for which, w= 16 rad/s when θ = 0 and θ = 6 radians when w= 0. Then determine the angular velocity when θ = 1.2 radians.
т A cylinder moves outward along the spinning platform with a speed of r = (5 · t) where t is in rad seconds. The platform rotates at a constant angular velocity of 0 = (3) Assume the cylinder starts from rest at the center. Using cylindrical coordinates, a. Determine the cylinders's radial and transverse components of velocity at t = 5 s, vr and ve. b. Determine the cylinders's radial and transverse components of acceleration at t = 5 s, ar and ae. c. Determine the cylinder's magnitude of the velocity at t = 5 s, v d. Determine the cylinder's magnitude of the acceleration at t = 5 s, a
Arm AB has a constant angular velocity of 800 rpm clockwise. determine the acceleration of the piston P when 0 = 60°. P D 50 mm 150 mm B
= At the instant shown rod AB has an angular velocity WAB 4 rad/s and an angular acceleration AB 2 rad/s2. Determine the angular velocity and angular acceleration of rod CD at this instant. The collar at C is pin connected to CD and slides freely along AB. = a) using the relative motion analysis and the contact conditions. A 4 rad/s AB= 2 rad/s² WAB 60° 0 = 0.75 m -0.5 m В B D
The vertical rod has a downward velocity v = 1.6 ft/sec and an upward acceleration a = 4.7 ft/sec? when the device is in the position shown. Determine the corresponding angular acceleration of bar AB (positive if counterclockwise, negative if clockwise) and the magnitude of the acceleration of roller Bif R = 19 in. A 1.35R 29° B Answers: a = i -13.97 rad/s2 aB = i ft/sec? -29.85 !!