You installed a single rope swing made of a wooden disc in the backyard of your house. Assuming you pulled the swing outward by a horizontal force u until the rope makes an angle of O degrees with the vertical (see diagram)
You installed a single rope swing made of a wooden disc in the backyard of your house. Assuming you pulled the swing outward by a horizontal force u until the rope makes an angle of O degrees with the vertical (see diagram)
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Transcribed Image Text:1 lb
Transcribed Image Text:You installed a single rope swing made of a wooden disc in the backyard of your house.
Assuming you pulled the swing outward by a horizontal force u until the rope makes an angle of
O degrees with the vertical (see diagram)
1 lb
a) Determine the resulting tension in the rope and the magnitude of u when 0
30°.
b) Write the tension T in the rope and the magnitude of u as functions of 0. Determine the
domains of the functions
c) Use a graphing utility to complete the table.
0°
10°
200
30°
400
50°
600
||u||
d) Use a graphing utility to graph the two functions for 0 < 0< 60.
e) Compare T and ||u|| as 0 increases
f) Find (if possible) T and ||u||
g) Are the results what you expected? Explain.
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