Will the rope break when the man swings?

AI Thread Summary
A man swinging from a 10-foot rope with a mass of 80 kg reaches a speed of 8 m/s at the bottom of his swing. The centripetal force calculated is 1678 N, but this does not account for his weight. The total tension in the rope at the bottom combines the centripetal force and the weight, leading to a tension of approximately 2460 N. This exceeds the rope's maximum tension limit of 2000 N, indicating that the rope will break. Therefore, the man does not make it safely.
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Homework Statement



a man swings from a rope which is 10 feet long. his mass is 80 kg and at the bottom of his swing, he is going 8 m/s. The max tension the rope can take without breaking is 2000 N. Does he make it?

Homework Equations



Fc = mv^2/r

The Attempt at a Solution



first i had to convert the feet to meters (3.05m). then i think the way to solve it is to first figure out the centripetal force generated by swinging - this would be (80 kg)(8)^2/(3.05 m) = 1678 N.

does this mean he's ok because the tension in the string doesn't exceed the 2000 N limit or do I need to include his weight in the problem?
 
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You already have his weight in the problem with 80kg
 
i konw but how do i put it into the calculations? so far all i figured out was the centripetal force?

how does the centripetal force, tension and his weight relate to each other at the bottom (when he's going 8 m/s)?
 
anyone?
 
another bump - still confused.

at the bottom of his swing, how does the centripetal force, tension force and his weight relate to each other?

i know weight points up and centripetal force points towards the middle (therefore up), but tension? i think it points up as well so would the equation be:

T + Fc - W = ma?
 
10 feet = 3.05m
and T_{max}=2000N

At the bottom;
\frac{mv^2}{{r}} = F_{T} - mg
hence
F_{T} = \frac{mv^2}{{r}} + mg

(If you need more clarification; http://dev.physicslab.org/Document.aspx?doctype=3&filename=OscillatoryMotion_VerticalCircles.xml)

Now you have your mass, radius and velocity given to you.
Using this equation, you should be able to simply plug the values in and get something in the league of 2.46x10^3 N

This is more than the maximum tension of 2000N, meaning that the rope will collapse.

Hope this helps
Steven
 
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