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

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To calculate the tension in the rope when a 30.8 kg child swings at the bottom of a 6.28 m rope with a speed of 4.2 m/s, both gravitational and centripetal forces must be considered. The centripetal acceleration is calculated using the formula a = (v^2)/r, leading to a force of 86.51 N. The gravitational force acting on the child is 301.84 N. The total tension in the rope combines these forces, resulting in a tension of approximately 388.35 N. This analysis highlights the importance of understanding the dynamics of circular motion in solving such problems.
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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.

\Sigma F = ma

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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