a. Explanation Given data: Mass of the flea ( m ) is 0.50 mg, which is written as ( 0.50 × 10 − 3 ) kg . Height reached by the flea in the absence of air resistance is 40 cm. Height reached by the flea in the presence of air resistance is 20 cm. Formula used: Write the expression for conservation of energy under no air resistance as follows. K i + ( U g ) i = K f + ( U g ) f (1) Here, K i is the initial kinetic energy of the flea, ( U g ) i is the initial gravitational potential energy, K f is the final kinetic energy, and ( U g ) f is the final gravitational potential energy. Write the expression for kinetic energy. K = 1 2 m v 2 (2) Here, m is the mass of the object, and v is the velocity (speed) of the object. Write the expression for gravitational potential energy. U g = m g y (3) Here, g is the acceleration due to the gravity, which is 9.8 m s 2 , and y is the height. Explanation: The presence of air resistance influences the transformation of energy. When the flea jumps under air resistance, the kinetic energy is transformed to thermal and potential energy. When the air resistance is not existed, the kinetic energy is only transformed to potential energy. Consider air resistance is not existed. Therefore, the flea is able to jump 40 cm. Calculation of initial kinetic energy: Consider the initial velocity (speed) of the flea as v . Modify the expression in equation (2) to find the initial kinetic energy of the flea as follows. K i = 1 2 m ( v i ) 2 Substitute ( 0.50 × 10 − 3 ) kg for m , and v for v i , K i = 1 2 ( 0.50 × 10 − 3 kg ) ( v ) 2 K i = ( 0.25 × 10 − 3 ) v 2 kg (4) Calculation of final kinetic energy: When the flea is reached to its maximum height (40 cm), it loses its complete velocity. Therefore, the final velocity of flea is 0 m s . Modify the expression in equation (2) to find the final kinetic energy of the flea as follows. K f = 1 2 m ( v f ) 2 Substitute ( 0.50 × 10 − 3 ) kg for m , and 0 m s for v f , K f = 1 2 ( 0.50 × 10 − 3 ) kg ( 0 m s ) 2 = 0 kg ⋅ m 2 s 2 { ∵ 1 kg ⋅ m 2 s 2 = 1 J } = 0 J Calculation of initial gravitational potential energy: As the flea initially at the ground, the initial height is 0 m. Modify the expression in equation (3) to find the initial gravitational potential energy of the flea as follows. ( U g ) i = m g y i Substitute ( 0.50 × 10 − 3 ) kg for m , 9.8 m s 2 for g , and 0 m for y i , ( U g ) i = ( 0.50 × 10 − 3 ) kg ( 9 b. To determine To find: The fraction of converted potential energy from the initial kinetic energy at the highest point of jump of the flea.

College Physics: A Strategic Approach Technology Update, Books a la Carte Plus Mastering Physics with Pearson eText -- Access Card Package (3rd Edition)

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ISBN: 9780134201979

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Chapter 10, Problem 56GP

To determine

To find: The kinetic energy of the flea when it leaves from the ground.

To determine

To find: The fraction of converted potential energy from the initial kinetic energy at the highest point of jump of the flea.

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Chapter 10, Problem 55GP

Chapter 10, Problem 57GP

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College Physics: A Strategic Approach Technology Update, Books a la Carte Plus Mastering Physics with Pearson eText -- Access Card Package (3rd Edition)

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The kinetic energy of the flea when it leaves from the ground.

Solution Summary: The author explains the kinetic energy of the flea when it leaves from the ground and the expression for conservation of energy under no air resistance.

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To find: The kinetic energy of the flea when it leaves from the ground.

To find: The fraction of converted potential energy from the initial kinetic energy at the highest point of jump of the flea.

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Chapter 10 Solutions