Explanation Given data: The height at which the divers dive to the water surface ( y ) is 35 m. Formula used: From the given data, the system is an isolated system. Refer to the equation (10.20) in the textbook, and modify the expression for conservation of energy for the given system as follows. K i + ( U g ) i = K f + ( U g ) f + Δ E th (1) Here, K i is the initial kinetic energy of the divers, ( U g ) i is the initial gravitational potential energy of the divers, K f is the final kinetic energy of the divers, ( U g ) f is the final gravitational potential energy of the divers, Δ E th is the change in thermal energy. Refer to the equation (10.8) in the textbook, and write the expression for kinetic energy of the divers as follows. K = 1 2 m v 2 (2) Here, m is the mass of the divers, and v is the velocity (speed) of the divers. Refer to the equation (10.14) in the textbook, and write the expression for gravitational potential energy as follows. 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 at which the divers dive to the water surface. Explanation: Consider the mass of the divers as m . From the given data, the diver is initially at rest in the perch. Therefore, the initial speed of the diver is 0 m s . v i = 0 m s The initial height is given as 35 m. y i = 35 m As the diver reaches to the surface of the water, the height become 0 m. Therefore, the final height is 0 m. y f = 0 m As there frictional force is not given in the system, the thermal energy during the diver’s dive from perch to the water surface is 0 J. Δ E th = 0 J Calculation of initial kinetic energy: Modify the expression in equation (2) to find the initial kinetic energy of the diver as follows. K i = 1 2 m ( v i ) 2 Substitute m for m , and 0 m s for v i , K i = 1 2 ( m ) ( 0 m s ) 2 = 0 J Calculation of final kinetic energy: Modify the expression in equation (2) to find the final kinetic energy of the diver as follows. K f = 1 2 m ( v f ) 2 Calculation of initial gravitational potential energy: Modify the expression in equation (3) to find the initial gravitational potential energy of the diver as follows. ( U g ) i = m g y i Substitute m for m , 9.8 m s 2 for g , and 35 m for y i , ( U g ) i = ( m ) ( 9.8 m s 2 ) ( 35 m ) = 343 m m 2 s 2 Calculation of final gravitational potential energy: Modify the expression in equation (3) to find the final gravitational potential energy of the diver as follows

16th Edition

ISBN: 9781323515303

Author: Knight

Publisher: PEARSON C

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Question

Chapter 10, Problem 36P

To determine

To find: The speed of the cliff divers when they reach the water surface and to explain the energy transformation as the cliff divers slow to a stop in the water.

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Chapter 10, Problem 35P

Chapter 10, Problem 37P

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