Explanation Given information: The weight of the crate ( W ) is 400 lb . The deceleration of the cable A ( a A ) y is 3 ft / s 2 . The deceleration of the cable B ( a B ) y is 1 ft / s 2 . The height of the crate ( w ) is 6.6 ft . The width of the crate ( h ) is 3.6 ft . Calculation: Consider the acceleration due to gravity ( g ) as 32.2 ft / s 2 . Calculate the mass of the crate ( m ) : m = W g Substitute 400 lb for W , and 32.2 ft / s 2 for g . m = 400 32.2 lb ⋅ s 2 / ft Calculate the mass moment of inertia of the crate ( I ¯ ) : I ¯ = 1 12 m ( w 2 + h 2 ) Substitute 400 32.2 lb ⋅ s 2 / ft for m , 6.6 ft for w , and 3.6 ft for h . I ¯ = 1 12 × 400 32.2 × ( 6.6 2 + 3.6 2 ) = 58.5093 lb ⋅ s 2 ⋅ ft Show the free body diagram of the crate as in Figure 1. Here, T A is the tension of the cable A , T B is the tension of the cable B , a is the acceleration of the crate, and α is the angular acceleration of the crate. Refer to Figure 1. Calculate the vertical forces by applying the equation of equilibrium: ∑ F y = m a T A + T B − W = m a Substitute 400 lb for W and 400 32.2 lb ⋅ s 2 / ft for m . T A + T B − 400 = 400 a 32.2 T A + T B = 400 a 32.2 + 400 T A + T B = 400 × ( a 32.2 + 1 ) (1) Calculate the moment about point G by applying the equation of equilibrium: ∑ M G = I G α ( T A − T B ) × 3.3 = I ¯ α Substitute 58.5093 lb ⋅ s 2 ⋅ ft for I ¯ . ( T A − T B ) × 3.3 = 58.5093 × α T A − T B = 58.5093 α 3.3 T A − T B = 17.73 α (2) Show the kinematic diagram of the crate as in Figure 2. Here, ( a A ) y is the deceleration of the cable A at y direction, ( a A ) x is the deceleration of the cable A at x direction, ( a B ) y is the deceleration of the cable B at y direction, and ( a B ) x is the deceleration of the cable B at x direction

12th Edition

ISBN: 9781260804638

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Videos

Question

Chapter 16.1, Problem 16.61P

To determine

Find the tension in each cable A (TA) and B (TB)

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.1, Problem 16.60P

Chapter 16.1, Problem 16.62P

Students have asked these similar questions

< 7:19 The 1st homework 6. Multiple Choice a)唧筒机构 5G31 Which of followings can be th e kinematic diagram of this mechanism? A B D

2:54 The 1st homework . 5G 27 b)回转柱塞泵机构 Which of followings can be the kinematic diagram of this mechanis m? A B D C

Im struggling to find the moment about point D. Please explain how to set up and solve

Chapter 16 Solutions

VECTOR MECHANICS FOR ENGINEERS W/CON >B

Ch. 16.1 - Two pendulums, A and B, with the masses and...Ch. 16.1 - Two pendulums, A and B, with the masses and...Ch. 16.1 - Two solid cylinders, A and B, have the same mass m...Ch. 16.1 - Prob. 16.1FBP Ch. 16.1 - Prob. 16.2FBP Ch. 16.1 - Prob. 16.3FBP Ch. 16.1 - The 400-lb crate shown is lowered by means of two...Ch. 16.1 - A 60-lb uniform thin panel is placed in a truck...Ch. 16.1 - A 60-lb uniform thin panel is placed in a truck...Ch. 16.1 - A loading car is at rest on a track forming an...

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.

Find the tension in each cable A ( T A ) and B ( T B )

Solution Summary: The author calculates the tension in each cable A (T_A) and B

Concept explainers

Videos

Find the tension in each cable A (TA) and B (TB)

Want to see the full answer?

Chapter 16 Solutions