# Circular Motion -- Swinging keys on a string in a vertical circle

• dylanjames
In summary: I'm not sure what the original question was. Sorry, you're right. I'm not sure what the original question was.
dylanjames

## Homework Statement

Assuming the keys are moving in uniform circular motion![/B]
Keys with a combined mass of 0.100 kg are attached to a 0.25 m long string and swung in a circle in the vertical plane.

a)What is the slowest speed that the keys can swing and still maintain a circular path?

b)What is the tension in the string at the bottom of the circle?

## Homework Equations

Given: V =10m/s, R=25m, Fc = mv^2/r, Ff = UFn[/B]
a) Centripetal Force is Fg, so Fg = MV^2/r
So, mg = mV^2/r
0.1(9.8) = (0.1)(V^2/0.25)
Mass cancels out..
9.8 = V^2/0.25
So, (0.25)(9.8) = V^2
Therefore, V^2 = 2.45, so V = 1.56m/s
The slowest speed the keys can travel and still maintain circular motion is 1.56m/s.

b) b) Fnet = Ft - Fg or Ft = Fnet + Fg (assuming this is uniform circular motion!)
Ft = mV^2/r + mg
Ft = [ (0.1)(1.56)^2 / 0.25 ] + (0.1)(9.8)
Ft = 0.97N
Therefore, assuming that the keys are moving in uniform circular motion, the Ft at the bottom of the circle is 0.97N.

Ok.. Really having a tough time with this one.
Been looking over it for too long and eyes are gone blurry.. any help is appreciated!

dylanjames said:
Ft = [ (0.1)(1.56)^2 / 0.25 ] + (0.1)(9.8)
Ft = 0.97N
Some mistake there, surely.

At the top it has a certain velocity, but you need to think about what happens as it goes downward (following the circular path).

you can't assume uniform circular motion in this case . it gains kinetic energy at the bottom

throneoo said:
you can't assume uniform circular motion in this case . it gains kinetic energy at the bottom
Judging from the calculations, dylanjames was not really assuming uniform circular motion, merely moving in a circle.

haruspex said:
Judging from the calculations, dylanjames was not really assuming uniform circular motion, merely moving in a circle.
if he wasn't why would he use the result from a) in b) for the keys' velocity at the bottom? I'm a bit confused here .

throneoo said:
if he wasn't why would he use the result from a) in b) for the keys' velocity at the bottom? I'm a bit confused here .
Sorry, you're right.

## 1. What is circular motion?

Circular motion is a type of motion in which an object moves along a circular path, with a constant speed and a changing direction.

## 2. How do swinging keys on a string in a vertical circle demonstrate circular motion?

When the keys are swung on a string in a vertical circle, they are constantly changing direction while maintaining a constant speed. This is a characteristic of circular motion, as the object is moving along a circular path.

## 3. Why do the keys on a string need to be swung in a vertical circle?

The vertical circle allows for the keys to experience a constant force of gravity pulling them towards the center, creating a circular motion. This is necessary for demonstrating circular motion and for the keys to maintain a constant speed.

## 4. What factors affect the speed of the keys in circular motion?

The speed of the keys in circular motion is affected by the length of the string, the mass of the keys, and the radius of the circle. A longer string or a smaller radius will result in a higher speed, while a shorter string or a larger radius will result in a lower speed.

## 5. How does centripetal force play a role in circular motion?

Centripetal force is the force that pulls objects towards the center of a circular path. In the case of swinging keys on a string in a vertical circle, the tension in the string acts as the centripetal force, keeping the keys moving along the circular path.

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