(a) Explanation Given info: The height of the balloon from the ground is 65.0 m , height of harness from the ground is 10.0 m , length of the cord is 5.0 m , length of the cord after the weight is tied is 1.50 m . The formula to calculate the force acting on the person is, F = m a (1) Here, m is the mass of the person. a is the acceleration. The formula to calculate the net force acting on the person in the elongation of the cord is, F = ( m g − k x ) l ′ (2) Here, m is the mass of the person. k is the force constant. g is the acceleration due to gravity. l ′ is the length of the cord. x is the length of elongation of cord. Equate the formula (1) and (2). m a = ( m g − k x ) l Substitute 0 for a , 1.50 m for x , l ( 5.0 m ) for l ′ in the above expression to find k . m a = ( m g − k x ) l ′ ( m g − k x ) l = 0 k = m g ( 5.0 m ) ( 1.50 m ) l = ( 3.33 ) m g l Thus, the value of k is ( 3.33 ) m g l . The formula to calculate the initial kinetic energy of the block is, K . E 1 = 1 2 m v 1 2 Here, m is the mass of the person. v 1 is the initial velocity. The initial speed of the person is 0 as the person is at rest then the initial kinetic energy of the person is 0. Substitute 950 kg for m and 0 for v 1 in the above formula to find K . E 1 . K . E 1 = 1 2 m v 1 2 = 1 2 ( m ) ( 0 ) 2 = 0 J Thus, the initial kinetic energy of the person is 0. The formula to calculate the final kinetic energy is, K . E 2 = 1 2 m v 2 2 Here, m is the mass of the person. v 2 is the final velocity of the person. The final velocity of a person is 0 as he stops by the harness above the ground then its final kinetic energy is 0. Substitute 0 for v 2 in the above formula to find K . E 2 . K . E 2 = 1 2 m v 2 2 = 1 2 m ( 0 ) 2 = 0 J Thus, the final kinetic energy of the person is 0 J . The formula to calculate the total kinetic energy is, K . E = K . E 2 + K . E 1 Here, K . E 2 is the final kinetic energy. K . E 1 is the initial kinetic energy. Substitute 0 for K . E 1 and 0 for K . E 2 in the above formula to find Δ K . E . Δ K . E = K . E 2 − K . E 1 = ( 0 J ) + ( 0 J ) = 0 J Thus, the total kinetic energy is 0 J . The formula to calculate the initial potential energy is, P . E 1 = m g ( h − 10.0 m ) Here, m is the mass of the person. h is the initial height of the balloon from the ground. Substitute 65.0 m for h in the above formula to find P . E 1 . P . E 1 = m g ( h − 10.0 m ) = m g ( 65.0 m − 10 .0 m ) = m g ( 55.0 m ) Thus, the initial potential energy is m g ( 55.0 m ) . The formula to calculate the final potential energy is, P . E 2 = 1 2 k ( h − 10.0 m − l ) 2 Here, k is the force constant (b) To determine The maximum acceleration.

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN: 9781305116399

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 8, Problem 8.85CP

(a)

To determine

The length of cord that should be used.

(b)

To determine

The maximum acceleration.

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Chapter 8, Problem 8.84CP

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Physics for Scientists and Engineers, Technology Update (No access codes included)

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The length of cord that should be used.

Solution Summary: The author explains the formula to calculate the force acting on the person in the elongation of the cord.

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The length of cord that should be used.

The maximum acceleration.

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Chapter 8 Solutions