(a) Explanation Given information: The mass ( m ) of the child is 20 kg. The speed ( v 0 ) .of the mother and child is 7.2 km/h. The average force ( T ) on the rope is 7 N. The coefficient of kinetic friction ( μ k ) between the child and the ground is 0.1. Calculation: Sketch the free body diagram and kinetic diagram of the child as shown in Figure (1). Here, m is the mass of the child, N is the normal force on the child, and a is the deceleration of the child. Refer Figure (1), Find the normal force ( N ) on the child. Apply Newton’s law of equation along y -axis (Consider positive along y -axis). N − m g cos 5 ° + T sin ( 20 ° − 5 ° ) = 0 Substitute 20 kg for m , 9.81 m/s 2 for g , and 7 N for T . N − m g cos 5 ° + T sin ( 20 ° − 5 ° ) = 0 N − ( 20 ) ( 9.81 ) cos 5 ° + ( 7 ) sin 15 ° = 0 N − 195.4534 + 1.8117 = 0 N = 193.64 N Find the deceleration ( a ) of the child. Apply Newton’s law of equation along x -axis (Consider positive along opposite to x -axis). m g sin 5 ° − μ k N − T cos ( 20 ° − 5 ° ) = m a Substitute 20 kg for m , 9.81 m/s 2 for g , 193.64 N for N , 0.1 for μ k , and 7 N for T . ( 20 ) ( 9.81 ) sin 5 ° − ( 0.1 ) ( 193.64 ) − ( 7 ) cos ( 20 ° − 5 ° ) = ( 20 ) a 17 (b) To determine The distance traveled when the child’s speed to be cut in half.

11th Edition

ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 12.1, Problem 12.10P

(a)

To determine

The time required for the child’s speed to be cut in half.

(b)

To determine

The distance traveled when the child’s speed to be cut in half.

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Chapter 12.1, Problem 12.9P

Chapter 12.1, Problem 12.11P

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