Solving Tension in Chain Homework

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SUMMARY

The discussion focuses on calculating the tension in a chain supporting a rider's chair attached to a rotating tower in an amusement park ride. The chair is connected by a 9.0-meter chain and rotates at a rate of 1 revolution every 4.0 seconds, with a maximum weight of 150 kg. The chain is rated to withstand a tension of 3000 N. To determine if the chain is strong enough, participants suggest using equations for centripetal force and vertical forces, emphasizing the need for a 3-D free body diagram to visualize the forces acting on the system.

PREREQUISITES
  • Centripetal force calculations
  • Understanding of tension in physics
  • Knowledge of free body diagrams
  • Basic trigonometry for resolving forces
NEXT STEPS
  • Calculate the centripetal acceleration using the formula a = v²/r
  • Learn how to derive tension using T = Fr/cos(theta)
  • Study the principles of rotational motion and angular velocity
  • Explore the construction and analysis of free body diagrams in 3-D systems
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Physics students, engineering students, and professionals involved in mechanical design or amusement park ride safety assessments.

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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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