Explanation Given data: Refer to the Figure P10.79 in the textbook for movement of the sledder. From the Figure, the height of the first hill is 4.2 m. Height of the second hill is 5.9 m. From the figure, the final velocity (speed) of the sledder ( v f ) at the highest point of second hill is 0 m s since the sledder loses complete velocity at the highest point of second hill. 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 (at the starting point of the sledder), ( U g ) i is the initial gravitational potential energy, K f is the final kinetic energy (at the highest point of the second hill), 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: Consider the mass of the sledder as m . Consider initial velocity of the sledder at his starting point as v 0 , which is to be determined. Consider the final velocity of the sledder at the highest point of the second hill as v 1 , which is 0 m s since the sledder loses his complete velocity at the highest point of second hill. Consider the initial height at his starting point as reference and consider the height as 0 m. Consider the final height of the sledder at the highest point of the second hill as y 1 , which is calculated as follows. Refer the Figure P10.79 in the textbook and write the mathematical expression to find the final height as follows. y 1 = h 2 − h 1 (4) Here, h 1 is the height of the first hill, which is 4.2 m, and h 2 is the height of the second hill, which is 5.9 m. Substitute 4.2 m for h 1 , 5.9 m for h 2 , y 1 = 5.9 m − 4.2 m = 1.7 m Therefore, the final height is 1.7 m. Calculation of initial kinetic energy: Modify the expression in equation (2) to find the initial kinetic energy of the sledder as follows. K i = 1 2 m ( v i ) 2 Substitute m for m , and v 0 for v i , K i = 1 2 ( m ) ( v 0 ) 2 = 0.5 m ( v 0 ) 2 Calculation of final kinetic energy: Modify the expression in equation (2) to find the final kinetic energy of the sledder as follows. K f = 1 2 m ( v f ) 2 Substitute m for m , and 0 m s for v f , K f = 1 2 ( m ) ( 0 m s ) 2 = 0 m m 2 s 2 Calculation of initial gravitational potential energy: Modify the expression in equation (3) to find the initial gravitational potential energy of the sledder as follows. ( U g ) i = m g y i Substitute m for m , 9

4th Edition

ISBN: 8220106755235

Author: Field

Publisher: PEARSON

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Question

Chapter 10, Problem 79GP

To determine

To find: The initial speed required for the sledder in order to reach the next hill.

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Chapter 10, Problem 78GP

Chapter 10, Problem 80GP

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