(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.

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ISBN: 8220100546310

Author: Jewett

Publisher: CENGAGE L

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The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The p…

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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

Chapter 9, Problem 9.1QQ

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Chapter 8 Solutions

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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 maximum acceleration.

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Chapter 8 Solutions