Solving Uniform Circular Motion: 0.150-kg Ball on a 1.10-m Cord

[Norngpinky]

Homework Statement

A 0.150-kg ball on the end of a 1.10-m-long cord (negligible mass) is swung in a vertical circle.

Homework Equations

Total net force = mass*centripetal acceleration = mass*(velocity squared)/radius

The Attempt at a Solution

The question I have is that... I'm looking at the book Physics Volume I, 6th Edition...And for the radius, shouldn't it be 1.10m/2 to get the radius? On the book, they just have 1.10m for r...So I'm confused here since I thought 1.10 is the diameter of the cord, not the radius. Could someone clarify that?

 

[Hootenanny]

Homework Statement

A 0.150-kg ball on the end of a 1.10-m-long cord (negligible mass) is swung in a vertical circle.

Homework Equations

Total net force = mass*centripetal acceleration = mass*(velocity squared)/radius

The Attempt at a Solution

The question I have is that... I'm looking at the book Physics Volume I, 6th Edition...And for the radius, shouldn't it be 1.10m/2 to get the radius? On the book, they just have 1.10m for r...So I'm confused here since I thought 1.10 is the diameter of the cord, not the radius. Could someone clarify that?

The radius is the distance from the centre of a circle to any point on the circumference. Now, when the ball is being swung in a vertical circle it is *always* on the circumference of the circular path, agreed? So, what is the distance between the ball and the centre of the circle?

 

[Norngpinky]

The radius is the distance from the centre of a circle to any point on the circumference. Now, when the ball is being swung in a vertical circle it is *always* on the circumference of the circular path, agreed? So, what is the distance between the ball and the centre of the circle?

Shouldn't it still be half the length of cord still since the center of the circle would be at the middle, so r should be half of the length...no?

 

[Hootenanny]

Shouldn't it still be half the length of cord still since the center of the circle would be at the middle, so r should be half of the length...no?

If you were swinging a ball around on a piece of string, at which point would you hold the string?

 

[Norngpinky]

If you were swinging a ball around on a piece of string, at which point would you hold the string?

AHA, that makes a lot more sense. So r would be the same even if the ball was in a horizontal circular motion, right?

 

[Hootenanny]

AHA, that makes a lot more sense. So r would be the same even if the ball was in a horizontal circular motion, right?

Correct. If the radius changed during the motion, then the ball would not be moving in a circle.

 

[Norngpinky]

Correct. If the radius changed during the motion, then the ball would not be moving in a circle.

Alright! You're awesome. Thank you for your help! =]