(a) Explanation Given information: The weight ( W A ) of the drum A is 1.4 lb. The radius of gyration ( k ¯ A ) of the drum A is 0.75 in.. The weight ( W B ) of the drum B is 3.5 lb. The radius of gyration ( k ¯ B ) of the drum B is 1.25 inch. The tension ( T A ) in the lower portion of the drum is 0.75 lb. The tape velocity ( v ) is 10 ft/s. The time ( t ) required to achieve tape velocity is 0.24 s. The radius ( r A ) of the drum A is 0.9 inch. The radius ( r B ) of the drum B is 1.5 inch. Calculation: Consider the drums A and B rotate about fixed axis. Find the angular velocity ( ω A ) of the drum A after 0.24 s using kinematics. v = r A ω A ω A = v r A Substitute 10 ft/s for v and 0.9 in. for r A . ω A = 10 ( 0.9 in . × 1 ft 12 in . ) = 133.333 rad/s Find the angular velocity ( ω B ) of the drum B after 0.24 s using kinematics. v = r B ω B ω B = v r B Substitute 10 ft/s for v and 1.5 in. for r B . ω B = 10 ( 1.5 in . × 1 ft 12 in . ) = 80 rad/s Find the mass ( m A ) of the drum A using the equation: m A = W A g Substitute 1.4 lb for W A and 32.2 ft/s 2 for g . m A = 1.4 32.2 = 0.04348 lb ⋅ s 2 /ft Find the mass ( m B ) of the drum B using the equation: m B = W B g Substitute 3.5 lb for W A and 32.2 ft/s 2 for g . m B = 3.5 32.2 = 0.1087 lb ⋅ s 2 /ft Find the mass moment of inertia ( I ¯ A ) of the drum A using the equation: I ¯ A = m A k A 2 Substitute 0.04348 lb ⋅ s 2 /ft for m A and 0.75 in. for k A . I ¯ A = 0.04348 × ( 0.75 in . × 1 ft 12 in . ) 2 = 169.844 × 10 − 6 lb ⋅ s 2 ⋅ ft Find the mass moment of inertia ( I ¯ B ) of the drum B using the equation: I ¯ B = m B k B 2 Substitute 0.1087 lb ⋅ s 2 /ft for m B and 1.25 in. for k B . I ¯ B = 0.1087 × ( 1.25 in (b) To determine Find the corresponding tension in the portion of tape between the drums.

12th Edition

ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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 17.2, Problem 17.64P

(a)

To determine

Find the required constant tension (TB) if the velocity of the tape is to be v=10 ft/s after 0.24 s.

(b)

To determine

Find the corresponding tension in the portion of tape between the drums.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17.2, Problem 17.63P

Chapter 17.2, Problem 17.65P

Students have asked these similar questions

answer this as soon as possible, please.

A piston–cylinder device contains 50 kg of water at 250 kPa and 25°C. The cross-sectional area of the piston is 0.1 m2. Heat is now transferred to the water, causing part of it to evaporate and expand. When the volume reaches 0.26 m3, the piston reaches a linear spring whose spring constant is 100 kN/m. More heat is transferred to the water until the piston rises 20 cm more. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the work done during this process. The work done during this process is kJ.

A 4-m × 5-m × 7-m room is heated by the radiator of a steam-heating system. The steam radiator transfers heat at a rate of 10,000 kJ/h, and a 100-W fan is used to distribute the warm air in the room. The rate of heat loss from the room is estimated to be about 5000 kJ/h. If the initial temperature of the room air is 10°C, determine how long it will take for the air temperature to rise to 25°C. Assume constant specific heats at room temperature. The gas constant of air is R = 0.287 kPa·m3/kg·K (Table A-1). Also, cv = 0.718 kJ/kg·K for air at room temperature (Table A-2). Steam enters the radiator system through an inlet outside the room and leaves the system through an outlet on the same side of the room. The fan is labeled as W sub p w. The heat is given off by the whole system consisting of room, radiator and fan at the rate of 5000 kilojoules per hour. It will take 831 Numeric ResponseEdit Unavailable. 831 incorrect.s for the air temperature to rise to 25°C.

Chapter 17 Solutions

VECTOR MECHANIC

Ch. 17.1 - A round object of mass m and radius r is released...Ch. 17.1 - Prob. 17.2CQ Ch. 17.1 - Prob. 17.3CQ Ch. 17.1 - Prob. 17.4CQ Ch. 17.1 - Slender bar A is rigidly connected to a massless...Ch. 17.1 - A 200-kg flywheel is at rest when a constant 300...Ch. 17.1 - The rotor of an electric motor has an angular...Ch. 17.1 - Prob. 17.3P Ch. 17.1 - Two disks of the same material are attached to a...Ch. 17.1 - The flywheel of a punching machine has a weight of...

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 required constant tension ( T B ) if the velocity of the tape is to be v = 10 ft/s after 0.24 s.

Solution Summary: The author calculates the angular velocity of the drums A and B after 0.24 s using kinematics.