Explanation Given data: Monica pulls her daughter Jessie in a bike trailer. Monica starts ups a 100 m long slope. Mass of the trailer and Jessie ( m ) is 25 kg. Distance of the slope ( d ) is 100 m. Height of the slope (height when the Monica reaches to the top) ( y f ) is 4.0 m. The constant force used by Monica to pull the bike trailer ( F ) is 8.0 N. Speed of the Monica along with the bike trailer and Jessie at the bottom of the slope ( v i ) is 5.3 m s . The initial height (at the bottom of the slope) ( y i ) is 0 m. Formula used: Write the expression for conservation of energy for the given system as follows. K i + ( U g ) i = K f + ( U g ) f + W (1) Here, K i is the initial kinetic energy (at the bottom of the slope), ( U g ) i is the initial gravitational potential energy, K f is the final kinetic energy (at the top of the slope), ( U g ) f is the final gravitational potential energy, and W is the work done by the Monica. Write the expression for kinetic energy. K = 1 2 m v 2 (2) Here, m is the mass of the trailer and Jessie, and v is the velocity (speed) of the Monica along with the bike trailer and Jessie. 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 of the slope. Write the expression for work done by the Monica as follows. W = F d (4) Here, F is the force used by Monica to pull the bike trailer, and d is the distance of the slope. Explanation: Consider the no frictional force in the given system. Therefore, the thermal energy in the system is zero. Calculation of initial kinetic energy at the bottom of the slope ( K i ) : Modify the expression in equation (2) for the initial kinetic energy at the bottom of the slope as follows. K i = 1 2 m ( v i ) 2 Substitute 25 kg for m , and 5.3 m s for v i , K i = 1 2 ( 25 kg ) ( 5.3 m s ) 2 = 1 2 ( 25 kg ) ( 28.09 m 2 s 2 ) = 351.125 kg ⋅ m 2 s 2 = 351.125 J { ∵ 1 kg ⋅ m 2 s 2 = 1 J } Calculation of final kinetic energy at the top of the slope ( K f ) : Modify the expression in equation (2) to find the final kinetic energy at the top of the slope as follows. K f = 1 2 m ( v f ) 2 Substitute 25 kg for m , K f = 1 2 ( 25 kg ) ( v f ) 2 = 12.5 ( v f ) 2 kg Calculation of initial gravitational potential energy: Modify the expression in equation (3) to find the initial gravitational potential energy as follows. ( U g ) i = m g y i Substitute 25 kg for m , 9

MODIFIED MASTERING COLLEGE PHYSICS 18WK.

4th Edition

ISBN: 9780136782216

Author: Knight

Publisher: PEARSON

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Question

Chapter 10, Problem 44P

To determine

To find: The speed of the Monica along with the bike trailer and Jessie at the top of the slope.

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Chapter 10, Problem 43P

Chapter 10, Problem 45P

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MODIFIED MASTERING COLLEGE PHYSICS 18WK.

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