8 A 25kg child sits on a rope swing. The rope has a length of L = 3m. The swing is moved so that it starts with an angle of 0 = 20°, and is released from rest. Looking at the image, the y direction will remained aligned with the string throughout its path. In this case, the acceleration in the y direction is always equal to v²/L, where v is the speed of the child. a. As soon as the swing is released, there is no acceleration in the y direction because the initial speed is 0. Calculate the acceleration in the a direction. (Draw a free body diagram, etc.) b. When the swing is at its lowest point, the swing will be moving with a speed of v = 1.88m/s. Calculate the force that the rope exerts on the swing when the swing is at its lowest point. (Draw another free body diagram, etc.)

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8 A 25kg child sits on a rope swing. The rope has a length of L = 3m. The
swing is moved so that it starts with an angle of 0 = 20°, and is released
from rest. Looking at the image, the y direction will remained aligned with
the string throughout its path. In this case, the acceleration in the y
direction is always equal to v²/L, where v is the speed of the child.
a. As soon as the swing is released, there is no acceleration in the y direction because
the initial speed is 0. Calculate the acceleration in the x direction. (Draw a free body
diagram, etc.)
b. When the swing is at its lowest point, the swing will be moving with a speed of v =
1.88m/s. Calculate the force that the rope exerts on the swing when the swing is at its
lowest point. (Draw another free body diagram, etc.)
Transcribed Image Text:8 A 25kg child sits on a rope swing. The rope has a length of L = 3m. The swing is moved so that it starts with an angle of 0 = 20°, and is released from rest. Looking at the image, the y direction will remained aligned with the string throughout its path. In this case, the acceleration in the y direction is always equal to v²/L, where v is the speed of the child. a. As soon as the swing is released, there is no acceleration in the y direction because the initial speed is 0. Calculate the acceleration in the x direction. (Draw a free body diagram, etc.) b. When the swing is at its lowest point, the swing will be moving with a speed of v = 1.88m/s. Calculate the force that the rope exerts on the swing when the swing is at its lowest point. (Draw another free body diagram, etc.)
OANSWERS
1 a. tf
1.27s; b. řf = -6.60mj, tf = 4.00s; c. V; = –3.50mj, ā =
%3D
2 half as much
3 they are all the same
4| car
5|a. 0.379m/s²-; b. 0.535m/s²÷; c. 4.17m/s²
6 a. 9.8m/s²1; b. 54.2m/s; c. 5.53s; d. 11.1m;
7 c. 2mm/ms?; d. (-2mm/ms)t + (1mm/ms²)ť²; e. 20.0N; f. (-2mm/ms) + (2mm/ms²)t; g.
2mm/ms;
8 a. 3.35m/s²; b. 275N;
Transcribed Image Text:OANSWERS 1 a. tf 1.27s; b. řf = -6.60mj, tf = 4.00s; c. V; = –3.50mj, ā = %3D 2 half as much 3 they are all the same 4| car 5|a. 0.379m/s²-; b. 0.535m/s²÷; c. 4.17m/s² 6 a. 9.8m/s²1; b. 54.2m/s; c. 5.53s; d. 11.1m; 7 c. 2mm/ms?; d. (-2mm/ms)t + (1mm/ms²)ť²; e. 20.0N; f. (-2mm/ms) + (2mm/ms²)t; g. 2mm/ms; 8 a. 3.35m/s²; b. 275N;
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