Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 9: Q8MCQ (page 230)
A woman is balancing on a high wire, which is tightly strung, as shown in Fig. 9鈥�45. The tension in the wire is
(a) about half the woman鈥檚 weight.
(b) about twice the woman鈥檚 weight.
(c) about equal to the woman鈥檚 weight.
(d) much less than the woman鈥檚 weight.
(e) much more than the woman鈥檚 weight.
Short Answer
The correct option is (e).
Step by step solution
Concepts
At equilibrium, the net force is zero. For this problem, find the condition for vertical forces.
Explanation
Let m be the mass of the woman and T be the tension in the wire.
At equilibrium for the vertical forces,
\(\begin{aligned}{c}T\sin \theta + T\sin \theta = mg\\2T\sin \theta = mg\\\sin \theta = \frac{{mg}}{{2T}}\end{aligned}\).
You can observe that the angle of the rope with the horizontal is very small and less than \({30^ \circ }\). Then,
\(\begin{aligned}{c}\sin \theta < \sin {30^ \circ }\\\frac{{mg}}{{2T}} < \frac{1}{2}\\T > mg\end{aligned}\).
Therefore, the tension in the wire is more than the woman鈥檚 weight.
Over 30 million students worldwide already upgrade their learning with 91影视!
