(a) Explanation Given information: The weight of the collar ( W ) is 8 oz . The radius of the semicircle ( r ) is 1.5 ft . The height of the point A to point C ( x ) is 7.5 ft . The acceleration due to gravity ( g ) is 32.2 ft / s 2 . The velocity of the package to hit C ( v C ) with a speed greater than 10 ft / s . The velocity at the point A is v 0 . Calculation: Consider the loop 1. Convert the unit of weight of the collar ( W ) from oz to lb using the relation: W = W oz 16 lb Here, W oz is the mass of the collar in oz . Substitute 8 oz for W oz . W = 8 16 = 0.5 lb Calculate the mass of the collar ( m ) using the formula: W = m g m = W g Substitute 0.5 lb for W and 32.2 ft / s 2 for g . m = 0.5 32.2 = 0.01553 lb ⋅ s 2 / ft Assume the datum is at position A . Show the free body diagram of the point B with the forces acting as in Figure (1). Calculate the velocity at B ( v B ) using the formula: v B = g r Substitute 32.2 ft / s 2 for g and 1.5 ft for r . v B = 32.2 ( 1.5 ) = 6.9498 ft / s Calculate the kinetic energy in the position B ( T B ) using the formula: T B = 1 2 m v B 2 Here, v B is the velocity at the point B . Substitute 0.01553 lb ⋅ s 2 / ft for m and 48.3 ft / s for v B . T B = 1 2 × 0.01553 × 48.3 ft / s = 0.37505 lb ⋅ ft Calculate the height at point B ( h ) using the relation: h = x + r Substitute 7.5 ft for x and 1.5 ft for r . h = 7 (b) To determine Find the largest allowable initial velocity ( v 0 ) .

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 13.2, Problem 13.75P

(a)

To determine

Show the requirements can be satisfied only by the second loop.

(b)

To determine

Find the largest allowable initial velocity (v0).

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Chapter 13.2, Problem 13.74P

Chapter 13.2, Problem 13.76P

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Show the requirements can be satisfied only by the second loop.

Solution Summary: The author shows the requirements can be satisfied only by the second loop, which does not work for the requirement.

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Show the requirements can be satisfied only by the second loop.

Find the largest allowable initial velocity (v0).

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