Circular Movement Homework: Part A Done, Part B Troubles

In summary: Therefore, we can ignore it in our energy conservation equation. This will give us a relation between the velocity and the angle of the ball's path.In summary, The problem at hand involves finding the tension as a function of angle, using a given equation and hint to express velocity squared as a function of angle. The velocity is not constant and can be found at any point using a given velocity at the top. Conservation of energy can be applied to find a relation between velocity and angle, and the tension force can be ignored as it does no work on the ball.
  • #1
asi123
258
0

Homework Statement



Everything is in the pictures.
I did part A, I have a problem with part B.
10x in advance.

Homework Equations





The Attempt at a Solution

 

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  • #2
You need to find the tension as a function of angle. (Forget the tension at the top.)

You have the correct equation. Hint: Express v^2 as a function of angle.
 
  • #3
Doc Al said:
You need to find the tension as a function of angle. (Forget the tension at the top.)

You have the correct equation. Hint: Express v^2 as a function of angle.

I know this equation (in the pic) but I'm doubtful if this what you meant...

Should I use trigo? can I get another tip :smile:?

10x.
 

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  • #4
The equation I had in mind was: mv^2/r = T + mg cos(theta).

Another hint: What's conserved as the ball continues on its path?
 
  • #5
Doc Al said:
The equation I had in mind was: mv^2/r = T + mg cos(theta).

Another hint: What's conserved as the ball continues on its path?

Ok, I already wrote that equation at the beginning in the solution part I uploaded and got stuck there.

I got stuck because I don't know the velocity at this point, I mean, the velocity is not constant, right? there is a mgsin(theta) that keep changing it...I think.

The velocity at the top is not the velocity at the bottom, right?

10x.
 
  • #6
asi123 said:
I got stuck because I don't know the velocity at this point, I mean, the velocity is not constant, right?
The velocity is definitely not constant. Reread my hint in post #4. :wink:

Given the velocity at the top, you should be able to find the velocity at any point as a function of angle.
 
  • #7
Doc Al said:
The velocity is definitely not constant. Reread my hint in post #4. :wink:

Given the velocity at the top, you should be able to find the velocity at any point as a function of angle.

:confused: I'm totally stuck, should I use trigo, or there is some equation for the velocity that I don't know about...

Oh, maybe u mean to use energy calculation?
 
  • #8
asi123 said:
Oh, maybe u mean to use energy calculation?
Getting warmer! :smile:
 
  • #9
Doc Al said:
Getting warmer! :smile:

The potential energy turns into kinetic energy, no?
 
  • #10
You got it. Keep going.
 
  • #11
Ok, I haven't really learned Conservation of energy so I'm not really familiar with it...

I wrote this equation about the energy, is it correct?

And another thing, What about T? it's not a Conservative force, right? Do I just ignore it in the the energy equation?

10x.
 

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  • #12
asi123 said:
Ok, I haven't really learned Conservation of energy so I'm not really familiar with it...

I wrote this equation about the energy, is it correct?
Looks good to me.
And another thing, What about T? it's not a Conservative force, right? Do I just ignore it in the the energy equation?
Excellent question! Ask yourself: Does the tension force do any work on the ball?
 
  • #13
Doc Al said:
Looks good to me.

Excellent question! Ask yourself: Does the tension force do any work on the ball?

Oh, right, it's vertical to his movement.

10x a lot.
 
  • #14
The ball's movement is always perpendicular to the tension, thus the tension does no work on the ball.
 

Related to Circular Movement Homework: Part A Done, Part B Troubles

1. What is circular movement and why is it important?

Circular movement is the motion of an object or particle along a circular path. It is important because it can be found in many natural phenomena, such as the orbit of planets around the sun, the rotation of the Earth, and the motion of electrons around an atom. It is also used in various machines and technologies, such as gears, pulleys, and centrifuges.

2. What is the difference between uniform circular motion and non-uniform circular motion?

Uniform circular motion is when an object moves along a circular path at a constant speed, while non-uniform circular motion is when the speed of the object changes at different points along the path. In uniform circular motion, the object experiences a constant centripetal acceleration, while in non-uniform circular motion, the acceleration varies in direction and magnitude.

3. How is centripetal force related to circular motion?

Centripetal force is the force that keeps an object in circular motion. It is always directed towards the center of the circular path and is equal to the product of the object's mass, its speed squared, and the radius of the circular path. Without a centripetal force, an object would continue in a straight line instead of following a circular path.

4. What are some real-life examples of circular motion?

Some real-life examples of circular motion include the motion of a Ferris wheel, the orbit of satellites around the Earth, the spin of a top, and the rotation of a ceiling fan. Other examples include the swinging of a pendulum, the motion of a car around a curve, and the motion of a planet around its star.

5. How can I solve problems involving circular motion?

To solve problems involving circular motion, you can use equations such as centripetal force = mass x speed² / radius, centripetal acceleration = speed² / radius, and velocity = 2πr / T (where r is the radius and T is the period). It is important to clearly define the variables and units in the problem and choose the appropriate equation to solve for the desired quantity.

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