CIRCULAR MOTION PROBLEM INVOLVING SPRING. In dire need of help please.

[jcfor3ver]

1. Homework Statement

A ball of mass m is connected by a spring shaft that is rotating with constant angular velocity (omega). A student looking down on the apparatus sees the ball moving counterclockwise in a circular path of radius r. When the spring is unstretched, the distance from the mass to the axis of the shaft is r sub o (little then subscript o). The orbital plane of the ball is height h above the ground. Suddenly the ball breaks loose from the spring , flies through the air, and hits the ground an unknown horizontal distance d from the point the ball breaks free from the spring. Let g be the magnitude of the acceleration of gravity. You may ignore air resistance or the size of the ball. Express your answers to the questions below in terms of the given numbers: m, omega, r, h, r sub o, and g as needed.

Here are the questions:
A) What is the magnitude of the spring constant k?
B) What is the magnitude of the velocity of the ball when it breaks free from the spring
C) How long does it take for the ball to hit the ground?
D) Find an expression for the horizontal distance the ball traveled from the point it breaks free from the spring until it hits the ground.

<< e-mail address deleted by Mentor >>

This problem deals with uniform circular motion, meaning the rpm speed is just 2 pi, or 2 pi r for velocity. I have to solve for it using just the letter notations, not number variables.



I am very confused and have this problem due in a few hours. If you could help me I would love it! I am just confused on how to tackle the problems, therefore I did not put up my mess of solutions. If I could get some feedback on how to do it that would be great! Thanks!

 

[jcfor3ver]

To figure out distance traveled, would I take Hooke's Law and multiply it by the velocity it was traveling when it got launched out of its circular path and then proceed with a 1d kinematic equation to find the distance?

 

[berkeman]

1. Homework Statement

A ball of mass m is connected by a spring shaft that is rotating with constant angular velocity (omega). A student looking down on the apparatus sees the ball moving counterclockwise in a circular path of radius r. When the spring is unstretched, the distance from the mass to the axis of the shaft is r sub o (little then subscript o). The orbital plane of the ball is height h above the ground. Suddenly the ball breaks loose from the spring , flies through the air, and hits the ground an unknown horizontal distance d from the point the ball breaks free from the spring. Let g be the magnitude of the acceleration of gravity. You may ignore air resistance or the size of the ball. Express your answers to the questions below in terms of the given numbers: m, omega, r, h, r sub o, and g as needed.

Here are the questions:
A) What is the magnitude of the spring constant k?
B) What is the magnitude of the velocity of the ball when it breaks free from the spring
C) How long does it take for the ball to hit the ground?
D) Find an expression for the horizontal distance the ball traveled from the point it breaks free from the spring until it hits the ground.

<< e-mail address deleted by Mentor >>

This problem deals with uniform circular motion, meaning the rpm speed is just 2 pi, or 2 pi r for velocity. I have to solve for it using just the letter notations, not number variables.



I am very confused and have this problem due in a few hours. If you could help me I would love it! I am just confused on how to tackle the problems, therefore I did not put up my mess of solutions. If I could get some feedback on how to do it that would be great! Thanks!

You should be able to start working out the questions symbollically. What are the relevant equations for uniform circular motion? What is Hooke's Law? Please start showing us your work on the questions...

 

[jcfor3ver]

For magnitude of spring constant I just did the F(restoring force)/deltax(displacementofspring)

For distance traveled I was thinking to use Vf^2=Vi^2+2*a*d and rearranging (since I do not know time) to get -Vi^2/2*a. Vf is 0 since that is when the ball hits the ground. I was thinking that my Vi would be taken from Hookes law of F=-k*deltax.

So Vi=omega*(-k*deltax). Am I on the right track?

 

[berkeman]

For magnitude of spring constant I just did the F(restoring force)/deltax(displacementofspring)

For distance traveled I was thinking to use Vf^2=Vi^2+2*a*d and rearranging (since I do not know time) to get -Vi^2/2*a. Vf is 0 since that is when the ball hits the ground. I was thinking that my Vi would be taken from Hookes law of F=-k*deltax.

So Vi=omega*(-k*deltax). Am I on the right track?

What is the relationship between rotational speed omega and centripetal force? How does that relate to the unstretched length and the stretched length of the spring?

 

[jcfor3ver]

What is the relationship between rotational speed omega and centripetal force? How does that relate to the unstretched length and the stretched length of the spring?

See that is my question, I am having a hard time figuring out this relationship. I am assuming that when the ball breaks from the spring the spring becomes unstretched, launching the ball, where the constant speed of omega is combined with the force the spring launches the ball at, which would become my Velocity initial in a kinematic equation. I just am unsure how to put my thoughts on paper.

 

[berkeman]

See that is my question, I am having a hard time figuring out this relationship. I am assuming that when the ball breaks from the spring the spring becomes unstretched, launching the ball, where the constant speed of omega is combined with the force the spring launches the ball at, which would become my Velocity initial in a kinematic equation. I just am unsure how to put my thoughts on paper.

Maybe that's why you are having trouble with the problem. I do not believe that the spring comes into play at all after it breaks. It only comes into play to help you define the position and initial velocity of the ball.

The stretching of the spring during the rotation tells you the centripetal force on the ball, via Hooke's Law. When the spring breaks, it just let's the ball go flying with a linear velocity defined by omega and the stretched radius. The spring does no "launching" when it breaks, it just let's the ball go.