(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.

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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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.

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Chapter 17.2, Problem 17.63P

Chapter 17.2, Problem 17.65P

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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.