Carnival ride : chair swings from cable attatched to overhang, spinning on axis

In summary, the problem involves finding the angle θ that a cable makes with the vertical axis when a chair is placed 10 m from a rotating vertical axis with a solid overhang stretching 6 meters from the axis. The chair spins at a constant speed of 1 revolution per 10 seconds. The equations used are ƩFr = mar = m(ω^2)r, ƩFz = maz, and ƩFt = mat = 0 (constant speed). Attempts at solving the problem involved analyzing the chair with the cable attached directly to the z axis and using trigonometry to find the angle β, which is equivalent to θ. However, it is found that the radius of revolution
  • #1
conorwood
5
0

Homework Statement



The chair is 10 m from the rotating vertical axis. The solid overhang stretches 6 meters from the axis. (making 4 m from end of overhang to chair on the radial axis). The chair spins at a constant speed at 1 revolution per 10 seconds. Find the angle θ the cable makes with the vertical axis.

Homework Equations



ƩFr = mar = m(ω^2)r
ƩFz = maz
ƩFt = mat = 0 (constant speed)

The Attempt at a Solution



I have not had troubles with the equation, but I have had issues setting up the problem.

I originally thought that I might be able to find θ if I analyzed the chair as if the cable was attached directly to the z axis. This would give me an angle let's call β. From here I could use trig to find θ. This is only true if the relationship between the situation where the cable is attached directly to the z axis and the situation where the cable is attached to the over hang looks like this:

|-\
|-β--\
|-------\
|----------\
|-------------\
|----------------\
|________________\
(sorry for the bad diagram. Its a triangle ignore the --)

where the bottom side is length 10 and

|-\
|-θ-\
|----\
|-----\
|------\
|-------\
|_______\

Where this bottom line is 4 and the heights are equal.

I doubt this is true. I would guess that the heights wouldn't be equal, and thus I would not be able to find θ this way.

My question is how I would find this true angle, or more generally, how would I deal with any radial problem where a mass is hung by a rope from a spot a certain distance x away from the center of the circle.

Thank you
 
Physics news on Phys.org
  • #2
hi conorwood! :smile:
conorwood said:
I originally thought that I might be able to find θ if I analyzed the chair as if the cable was attached directly to the z axis. This would give me an angle let's call β. From here I could use trig to find θ.

i think β and θ are the same

try solving the equations …

you'll probably find that the radius of revolution is the only length that matters :wink:
 

1. How do chair swings on carnival rides stay attached to the cable?

The chairs on a carnival ride are attached to the cable by strong metal clamps that securely lock onto the cable. These clamps are designed to withstand high speeds and forces, ensuring the safety of riders.

2. What keeps the chair swings from flying off the cable while spinning?

The angle at which the chairs are attached to the cable, combined with the centripetal force generated by the spinning motion, keeps the chairs securely in place. Additionally, there are safety measures in place such as seatbelts and lap bars to ensure riders stay in their seats.

3. How is the spinning motion controlled on chair swings?

The spinning motion of chair swings is controlled by a motor that is connected to the cable. The motor can be adjusted to change the speed and direction of the spinning, providing a thrilling and unique experience for riders.

4. Is it safe to ride chair swings on a carnival ride?

Yes, carnival ride manufacturers follow strict safety regulations and guidelines when designing and constructing chair swings. Additionally, regular maintenance and safety inspections are performed to ensure the safety of riders.

5. How fast do chair swings on carnival rides typically spin?

The speed of chair swings on carnival rides can vary, but they typically spin at speeds between 15-25 miles per hour. This speed is enough to provide a thrilling experience without compromising the safety of riders.

Similar threads

  • Introductory Physics Homework Help
Replies
22
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
4K
  • Introductory Physics Homework Help
Replies
19
Views
723
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
26
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
963
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
987
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top