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 (4th Edition)

4th Edition

ISBN: 9780134704180

Author: Knight

Publisher: PEARSON

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Power is defined in physics as the amount of energy transmitted or transformed per unit time. The watt is the unit of electricity in the International System of Units, equivalent to one joule per second.

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Chapter 10, Problem 75GP

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 74GP

Chapter 10, Problem 76GP

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College Physics: A Strategic Approach (4th 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