Calculating Tension: Child on a Swing with a 6.28m Rope | Find Tension in N

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Homework Help Overview

The problem involves calculating the tension in a rope from which a child swings, given the child's mass, the length of the rope, and the speed at the lowest point of the swing. The subject area pertains to dynamics and circular motion.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the forces acting on the child, including gravity and tension, and explore the relationship to circular motion. Questions are raised about applicable equations and the role of centripetal acceleration in the scenario.

Discussion Status

Some participants have provided insights into the forces involved and suggested relevant equations, while others are still seeking clarity on the concepts and calculations. There is an ongoing exploration of how to approach the problem without reaching a definitive conclusion.

Contextual Notes

There appears to be some uncertainty regarding the equations that should be applied, as well as the interpretation of the forces acting on the child during the swing.

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Homework Statement



A 30.8 kg child swings on a rope with a length of 6.28 m that is hanging from a tree. At the bottom of the swing, the child is moving at a speed of 4.2 m/s. What is the tension in the rope?
______ N


Homework Equations



?

The Attempt at a Solution



I know you are suppose to draw a FBD but I get stuck from there.
 
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what forces are acting on the child?

and what equations have you learned so far that deal with something that resembles swinging. if you draw out the swinging motion it's actually part of a larger circular motion.
 
Gravity is acting on the child. I think that's it. I don't know which equation woulud apply...thats why i put the ? haha
 
Jtappan said:
Gravity is acting on the child. I think that's it. I don't know which equation woulud apply...thats why i put the ? haha

you have tension and gravity acting on the child. think centripetal.

[tex]\Sigma F = ma[/tex]

what is a here? put the forces in the left side of the equation...
 
We find the centripetal acceleration at the bottom:

a = (v^2)/r

so

F= (mv^2)/r

Plug stuff in:

F = 86.51N

Now we add that to the gravitational force, which it must counteract:

F = m*9.80

F = 301.84N

And find the tension is:

3.9x10^2 N

(388.35 w/o sigfigs)
 

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