Solution Found!
You have a new job designing rides for an amusement park.
Chapter 8, Problem 44P(choose chapter or problem)
Problem 44P
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 1.0 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. Will this chain be strong enough for the ride?
Questions & Answers
QUESTION:
Problem 44P
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 1.0 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. Will this chain be strong enough for the ride?
ANSWER:
Step 1 of 3
We are going to check the tension in the chain and compare it to the rated maximum tension.
The length of the chain \(\mathrm{L}=9 \mathrm{~m}\)
The mass of the chair with the rider \(\mathrm{m}=150 \mathrm{~kg}\)
The angular speed \(\omega=1 \mathrm{rev} / 4 \mathrm{~s}\)
The rated tension \(\mathrm{T}_{\max }=3000 \mathrm{Naz}\)