Solving Tension in Chain Homework

In summary, the conversation discusses a new job designing amusement park rides and the question of whether a chain found at a discount store is strong enough for a ride where the rider's chair is attached to a rotating tower. The maximum combined weight of the chair and rider is 150 kg and the chain is rated to withstand a tension of 3000 N. The solution involves finding the tension and angle using equations for sum of horizontal and vertical forces and a 3-D free body diagram.
  • #1
holmeskaei
8
0

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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  • #2
How would you think to start to figure the Tension?

What forces must the chain handle?
 
  • #3
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.
 
  • #4
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
 
  • #5
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.
 

1. What is tension in a chain?

Tension in a chain refers to the force applied on the chain that causes it to stretch or become taut. It is an important concept in understanding the behavior of chains under different conditions.

2. How do I solve tension in chain homework problems?

The best way to solve tension in chain homework problems is to break it down into smaller steps. Start by drawing a free body diagram and identifying all the forces acting on the chain. Then use equations like Newton's second law and Hooke's law to calculate the tension in the chain.

3. What factors can affect tension in a chain?

There are several factors that can affect tension in a chain, including the weight of the object being lifted, the angle of the chain, the material and thickness of the chain, and the amount of force applied to the chain.

4. How does the angle of the chain affect tension?

The angle of the chain can greatly affect the tension in the chain. As the angle increases, the tension in the chain also increases. This is because the weight of the object being lifted is distributed over a longer length of the chain, requiring more tension to support it.

5. Can tension in a chain ever be greater than the weight of the object being lifted?

Yes, in certain situations, tension in a chain can be greater than the weight of the object being lifted. This can happen when the angle of the chain is close to 90 degrees, as the tension in the chain has to support not only the weight of the object but also the horizontal component of the force acting on it.

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