Solving Tension in Chain Homework

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To determine if the chain can withstand the tension from the ride, the first step is to calculate the velocity of the chair using the given rotation rate of 1 revolution every 4 seconds. The tension in the chain must be analyzed by considering both horizontal and vertical forces, requiring the use of two equations: one for centripetal force (mv²/r) and one for vertical equilibrium (sum of vertical forces equals zero). A 3-D free body diagram is essential for visualizing the forces acting on the chair and rider, including the gravitational force and the tension in the chain. The angle of the chain is also a critical factor, which can be derived from the geometry of the system. Ultimately, the calculated tension must be compared to the chain's maximum rating of 3000 N to ensure safety.
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Homework Statement



You have a new job designing rides for an amusement park. In one ride, the rider's chair is attached by a 9.0-m-long chain to the top of a tall rotating tower. The tower spins the chair and rider around at the rate of 1 rev every 4.0 s. In your design, you've assumed that the maximum possible combined weight of the chair and rider is 150 kg. You've found a great price for chain at the local discount store, but your supervisor wonders if the chain is strong enough. You contact the manufacturer and learn that the chain is rated to withstand a tension of 3000 N.

Is the chain strong enough?


Homework Equations


w=v/r
Fr=Tcos(theta)
Fz=n-Fg=0


The Attempt at a Solution


Find tension that is supported by the system, and compare it to the 3000N.
 
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How would you think to start to figure the Tension?

What forces must the chain handle?
 
I know that Fr=Tcos(theta)
Fz=n-Fg=0
So the T=Fr/cos(theta)
But I don't have an angle.
I have a radius, and I have a mass, and I can find a velocity using the 1 revolution=4.0 seconds.
I am not sure how to go about this.
 
You must write TWO equations to find the tension and the angle.
Sum of the horizontal forces = mv^2/r
Sum of the vertical forces = 0
 
The place to start this problem is with a 3-D free body diagram. Also, you need to be very clear on your definitions of r, theta, omega, etc.
 

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