Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 4 - Forces and Newton's Laws of Motion - Check Your Understanding - Page 110: 23

Answer

When she starts climbing, the tension in the rope is greater than when she hangs stationary.

Work Step by Step

When the circus performer hangs stationary from a rope, she is under the influence of her own weight $mg$ which points downward and the tension in the rope $T$ which points upward. Being stationary means there is no acceleration, so $$T=mg$$ When she starts climbing upward, she is still under the influence of the same 2 forces but now she has an upward acceleration $a$. According to Newton's 2nd law, we have $$T-mg=ma$$ $$T=m(g+a)$$ which is greater than $T$ when the performer is stationary. Therefore, when she starts climbing, the tension in the rope is greater than when she hangs stationary.
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