Centripetal force, enough information?

[Gauss M.D.]

Homework Statement

We have a carousel that completes a revolution in 4,0 s. The radius of the carousel disk is 0,8 m and the length of the (massless) rope is 1m. A horsey or whatever weighing 1 kg is hanging from the rope.

Can we from this information extract the velocity of the horsey?

Homework Equations

The Attempt at a Solution

I tried some trig manipulation but ran into trouble because I have the hypotenuse of one triangle in meters but the side of another in Newtons... I think I fried my brain attempting a solution.

 

[Joseph King]

You need to calculate the circumference of the circle using the radius. That will give you the distance that the whatever will travel in 4 seconds. Then divide that circumference by 4 to yield a velocity in meters per second.

 

[Gauss M.D.]

You need to calculate the circumference of the circle using the radius. That will give you the distance that the whatever will travel in 4 seconds. Then divide that circumference by 4 to yield a velocity in meters per second.

No the horseys path is much wider. It's hanging freely from the rope.

 

[Joseph King]

Then add the length of the rope to the radius of the carousel before calculating the circumference.

 

[Gauss M.D.]

The rope will be at an angle so that won't work.

 

[Joseph King]

The rope should not be at an angle unless the carousel is accelerating. If the speed at which the carousel remains constant, then the rope should be perpendicular to it.

 

[gneill]

The rope should not be at an angle unless the carousel is accelerating. If the speed at which the carousel remains constant, then the rope should be perpendicular to it.

Noooooooo!

 

[Joseph King]

Why no?

 

[gneill]

Why no?

Centripetal force / acceleration does not depend upon angular acceleration, it depends upon angular velocity.

 

[Joseph King]

That's what I was saying. I might have been a little unclear. Also, are we ignoring gravity? That would drastically change the question.

 

[hms.tech]

Assuming that there is no angular acceleration (ie the circular disk from which the horsey hangs is not accelerating).
First you must notice that the angular velocity of the of the system, the horsey and the disk is constant. To calculate this we use :

angular velocity = 2(pi)/4 rad per second

Can you work from here ?

 

[hms.tech]

That's what I was saying. I might have been a little unclear. Also, are we ignoring gravity? That would drastically change the question.

No we are not ignoring gravity, that is precisely why the string would be at an angle.
To help you visualize this better, if there were no gravity, the string would be at exactly zero degrees to the circular disk, in other words exactly parallel to the rotating disk, much like the Earth orbiting the sun .

 

[Joseph King]

Ah, I see. That changes everything.

 

[Gauss M.D.]

Assuming that there is no angular acceleration (ie the circular disk from which the horsey hangs is not accelerating).
First you must notice that the angular velocity of the of the system, the horsey and the disk is constant. To calculate this we use :

angular velocity = 2(pi)/4 rad per second

Can you work from here ?

No, I got that part down. Don't know where to proceed from there though! I think the centripetal force will be the vector sum of the force of gravity and the tension in the wire (am I wrong?). Don't know how to extract the force of tension with the information at hand though :S

 

[Doc Al]

No, I got that part down. Don't know where to proceed from there though! I think the centripetal force will be the vector sum of the force of gravity and the tension in the wire (am I wrong?). Don't know how to extract the force of tension with the information at hand though :S

Have you drawn a Free Body Diagram? And then applied Newton's 2nd law?

 

[Gauss M.D.]

Have you drawn a Free Body Diagram? And then applied Newton's 2nd law?

Don't I need to know the radius from the horsey to the center of the carousel to figure out the force acting on the horsey?

 

[Doc Al]

Don't I need to know the radius from the horsey to the center of the carousel to figure out the force acting on the horsey?

That's one of the things you can solve for. Express it as a function of the angle that the rope makes.

But in drawing a free body diagram, you'll only show the actual forces acting on the horsey. Hint: There are only two.