Accelaration in a vertical circle

In summary, the angle at which the string goes slack is 8 degrees. The string will remain slack for 3 seconds.
  • #1
mazz1801
23
0
A ball is attached to an inextensible string of negligable mass and hangs vertically under gravity. At time t=0, it is given a horizontal velocity u and begins to move in a vertical circle of radius r. At any time t>0, the ball is at an angle θ to the vertical and has a velocity v tangential to its circle of motion. There is no friction acting so that the mechanical energy of the ball is conserved/

If u=4rg, find the angle θ at which the string goes slack. For how long will the string remain slack before becoming taut again?

I'm having trouble even starting with this part of the question. (The first part was to prove that the difference in tension at the bottom and tension at the top was 6 times the weight of the ball- I got that bit)

I have tried using the equations for motion in a circle. Basically all of them and they are all leading me down the same street!

I'm pretty desperate here... could someone just tell me what equation I should be using!
Also will the answer be numerical or contain m and g...
 
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  • #2
mazz1801 said:
A ball is attached to an inextensible string of negligable mass and hangs vertically under gravity. At time t=0, it is given a horizontal velocity u and begins to move in a vertical circle of radius r. At any time t>0, the ball is at an angle θ to the vertical and has a velocity v tangential to its circle of motion. There is no friction acting so that the mechanical energy of the ball is conserved/

If u=4rg, find the angle θ at which the string goes slack. For how long will the string remain slack before becoming taut again?

I'm having trouble even starting with this part of the question. (The first part was to prove that the difference in tension at the bottom and tension at the top was 6 times the weight of the ball- I got that bit)

I have tried using the equations for motion in a circle. Basically all of them and they are all leading me down the same street!

I'm pretty desperate here... could someone just tell me what equation I should be using!

You are looking for the point at which the tension goes to zero. Since you must already know how to calculate the tension from the first part, that should be a hint.

However, are you sure you have the initial velocity correct? The units don't seem right to me.

Also will the answer be numerical or contain m and g...

How can you get a numerical answer if there are no numbers? Seriously. When I was a TA I would give quizzes with no numbers in them and get back numerical answers. How does that work?
 
  • #3
I made a mistake! Inital velocity is u2=4rg
I used the function wrong.

Also the unit thing must have been a blonde moment! Thanks for your help!
 

FAQ: Accelaration in a vertical circle

1. What is the definition of acceleration in a vertical circle?

Acceleration in a vertical circle refers to the rate of change of velocity in an object moving in a circular path in a vertical plane. It is a measure of how quickly the object's speed and/or direction is changing as it moves along the circular path.

2. How is acceleration in a vertical circle calculated?

The acceleration in a vertical circle can be calculated using the formula a = v^2/r, where "a" is the acceleration, "v" is the velocity, and "r" is the radius of the circular path. It can also be calculated using the formula a = (v^2 - u^2)/r, where "u" is the initial velocity.

3. What factors affect acceleration in a vertical circle?

The factors that affect acceleration in a vertical circle include the speed of the object, the radius of the circular path, and the direction of the object's motion. The greater the speed and/or the smaller the radius, the greater the acceleration will be. Additionally, the direction of the object's motion can also affect the acceleration if it changes during the circular path.

4. How does acceleration in a vertical circle differ from acceleration in a horizontal circle?

Acceleration in a vertical circle differs from acceleration in a horizontal circle in terms of direction. In a vertical circle, the acceleration is constantly changing as the object moves up and down, while in a horizontal circle, the acceleration remains constant because the direction of motion remains constant.

5. Why is acceleration in a vertical circle important?

Acceleration in a vertical circle is important because it helps us understand the motion of objects in circular paths, which is a common occurrence in many real-world scenarios such as roller coasters, carousels, and Ferris wheels. It also plays a crucial role in designing and analyzing the performance of various machines and vehicles that move in circular paths.

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