a. Explanation Given data: Mass of the skateboarder ( m ) is 55 kg. Final velocity (speed) of the skate boarder (speed at the top of the half-pipe) is 0 m s since he loses his complete velocity when he is coasted the up side of the pipe. Refer to the Figure P10.55 in the textbook for the coasting of skateboarder on the half-pipe. From the Figure, the height of the pipe from bottom (center of the pipe) to the top of the pipe is 3.0 m. Therefore, change in the height is 3.0 m. Formula used: Write the expression for conservation of energy for the given conditions as follows. K i + ( U g ) i = K f + ( U g ) f (1) Here, K i is the initial kinetic energy of the skateboarder (at the center of the pipe), ( U g ) i is the initial gravitational potential energy, K f is the final kinetic energy (when the skateboarder reaches the up side of the pipe), 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. From the given data, the skateboarder is at the center of the pipe. Therefore, consider the initial height as 0 m and final height when he is at the up side of the pipe as the 3.0 m. Consider the required initial speed of the skateboarder as v , which is to be determined. Calculation of initial kinetic energy: Modify the expression in equation (2) to find the initial kinetic energy of the skateboarder as follows. K i = 1 2 m ( v i ) 2 Substitute 55 kg for m , and v for v i , K i = 1 2 ( 55 kg ) ( v ) 2 = 1 2 ( 55 kg ) v 2 = 27.5 v 2 kg Calculation of final kinetic energy: Modify the expression in equation (2) to find the final kinetic energy of the skateboarder as follows. K f = 1 2 m ( v f ) 2 Substitute 55 kg for m , and 0 m s for v f , K f = 1 2 ( 55 kg ) ( 0 m s ) 2 = 0 kg ⋅ m 2 s 2 = 0 J Calculation of initial gravitational potential energy: Modify the expression in equation (3) to find the initial gravitational potential energy of the skateboarder as follows. ( U g ) i = m g y i Substitute 55 kg for m , 9 b. To determine To find: The initial speed required for the skateboarder to coast all the way up when he is at 0.75 m from the center of the pipe.

College Physics: A Strategic Approach (3rd Edition)

3rd Edition

ISBN: 9780321879721

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

Publisher: PEARSON

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Chapter 10, Problem 55GP

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To find: The initial speed at the bottom of the pipe required for the skateboarder to coast all the way up.

To determine

To find: The initial speed required for the skateboarder to coast all the way up when he is at 0.75 m from the center of the pipe.

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Chapter 10, Problem 54GP

Chapter 10, Problem 56GP

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College Physics: A Strategic Approach (3rd Edition)

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The initial speed at the bottom of the pipe required for the skateboarder to coast all the way up.

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To find: The initial speed at the bottom of the pipe required for the skateboarder to coast all the way up.

To find: The initial speed required for the skateboarder to coast all the way up when he is at 0.75 m from the center of the pipe.

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