How Does Vine Tension Affect Jill's Swing Dynamics?

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SUMMARY

The discussion focuses on calculating the tension in a vine when Jill, with a mass of 65 kg, swings at a speed of 2.4 m/s while the vine is vertical. The correct formula to determine tension is T = mg + mv²/r, where g is the acceleration due to gravity (9.81 m/s²) and r is the length of the vine (6.9 m). If Jill's mass is doubled, the tension in the vine increases significantly, affecting her vertical speed upon landing. The calculations reveal that the tension and velocity are directly influenced by changes in mass.

PREREQUISITES
  • Understanding of Newton's Second Law (T = mg + mv²/r)
  • Basic knowledge of kinematics and free body diagrams
  • Familiarity with gravitational acceleration (9.81 m/s²)
  • Concept of centripetal force in circular motion
NEXT STEPS
  • Calculate tension in various scenarios using different masses
  • Explore the effects of varying vine lengths on swing dynamics
  • Learn about energy conservation in pendulum motion
  • Investigate the impact of initial velocities on landing speed
USEFUL FOR

Physics students, educators, and anyone interested in understanding dynamics and forces in motion, particularly in pendulum-like systems.

MaggieNF
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Homework Statement


Jill of the jungle swings on a vine 6.9 m long (assume no friction)

what is the tension in the vine if jill, whose mass is 65 kg, is moving at 2.4m/s when the vine is vertical? Draw a free body diagram

Assume Jill stops holding on at exactly the moment the vine is vertical and lands on the ground exactly 2.5 seconds later. What is her vertical speed when reaching the ground?

How does the tension in the vine change if her mass is doubled? How does this effect her velocity when reaching the ground? explain

Homework Equations





The Attempt at a Solution



was thinking you could use T=ma.. thus 65* 2.4 =154 N
 
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Welcome to PF!

Hi MaggieNF! Welcome to PF! :wink:
MaggieNF said:
what is the tension in the vine if jill, whose mass is 65 kg, is moving at 2.4m/s when the vine is vertical? Draw a free body diagram
…
I was thinking you could use T=ma.. thus 65* 2.4 =154 N

but 2.4 is v, not a :redface:

you need to find the https://www.physicsforums.com/library.php?do=view_item&itemid=27" :smile:
 
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