# Swinging Ball at Top of Circle: Forces & Energies

In summary: For e, you could try doing a similar calculation to the one for gravity in a free-body diagram, but with the cord in addition to the weight.
1. A 0.160 kg ball attached to a light cord is swung in a vertical circle of radius 70.0 cm. At the top of the swing, the speed of the ball is 3.26 m/s. The centre of the circle is 1.50 m above the floor.
a. Draw a free-body diagram of the forces on the ball at the top of the swing.

b. Calculate the magnitude of the tension in the cord at the top of the swing.

c. With respect to the floor, calculate the mechanical energy of the ball at the top of the swing

d. Calculate the speed of the ball when the cord is 30.0̊ below the horizontal

e. Determine the magnitude of the tension in the cord when the cord is 30.0̊ below the horizontal

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You should probably maintain the format of the homework section or else moderators will remove it.

Zack K said:
You should probably maintain the format of the homework section or else moderators will remove it.
thanks for the headsup man. I'm currently updating it.

And we are awaiting your changes...

jedishrfu said:
And we are awaiting your changes...
okay give me some time geez

It's a bit of humor on my part...

Read my signature quote from Day the Earth Stood Still.

I'm a robot so what do you expect?

Zack K
Okay, so your free body diagram shows the rope tension going downward.

Is that right?

What happened to the homework template? You know the three questions that we ask?

jedishrfu said:
Okay, so your free body diagram shows the rope tension going downward.

Is that right?
yes, it does.

If I spin the weight in a vertical circle and let go, will the ball go up or drop down?

jedishrfu said:
If I spin the weight in a vertical circle and let go, will the ball go up or drop down?
drop because of gravity

Okay you're right about the tension.

jedishrfu said:
Okay you're right about the tension.
not sure if my diagram is 100% right, along with my answers for b and c. Also, how do I go about d and e?

Show us some work on d and e. Its a bit beyond what I can help with but some homework helper will sign on soon.

We can't always promise that questions will be answered quickly here especially on the weekend. It all depends on when our advisors and homework helpers sign on.

Try using the references I gave you and see if you can work it out.

I think I'm good for a) and b) because you sent me those links. although, I'm not sure on how to incorporate the angle in for d) and e)
For d, start with finding the energy at the top of the motion, then think of how you can use the idea of conservation of energy to solve it.

jedishrfu

## Q1: How does the swinging ball at the top of a circle demonstrate forces and energies?

The swinging ball at the top of a circle demonstrates forces and energies through the concept of centripetal force and potential and kinetic energies. As the ball swings around the circle, it experiences a centripetal force towards the center of the circle, keeping it in circular motion. This force is provided by the tension in the string or rope that the ball is attached to. At the top of the circle, the ball has maximum potential energy due to its height, and as it swings down, this potential energy is converted into kinetic energy, giving the ball speed. At the bottom of the circle, the ball has maximum kinetic energy and minimum potential energy.

## Q2: How does the radius of the circle affect the forces and energies of the swinging ball?

The radius of the circle affects the forces and energies of the swinging ball in two ways. First, the centripetal force required to keep the ball in circular motion is directly proportional to the mass of the ball and the square of the velocity, and inversely proportional to the radius of the circle. This means that a smaller radius requires a greater centripetal force, resulting in a higher tension in the string and greater potential and kinetic energies. Second, the height at which the ball is released also affects the potential and kinetic energies, as a larger radius means a greater height and therefore more potential energy at the top of the circle.

## Q3: Can the swinging ball at the top of a circle demonstrate other types of forces?

Yes, the swinging ball at the top of a circle can demonstrate other types of forces, such as centrifugal force and gravity. Centrifugal force is the apparent force that pushes an object away from the center of rotation, and in the case of the swinging ball, this force acts in the opposite direction of the centripetal force. Gravity also plays a role in the forces and energies of the swinging ball, as it pulls the ball towards the center of the Earth, affecting its potential and kinetic energies.

## Q4: How does the mass of the ball affect the forces and energies of the swinging ball?

The mass of the ball affects the forces and energies of the swinging ball through the concept of inertia. Inertia is the resistance of an object to changes in its state of motion, and in this case, it refers to the ball's resistance to changes in its circular motion. A heavier ball will have a greater inertia and therefore require a greater centripetal force to maintain its circular motion. This results in a higher tension in the string and greater potential and kinetic energies.

## Q5: Can the swinging ball at the top of a circle demonstrate conservation of energy?

Yes, the swinging ball at the top of a circle can demonstrate conservation of energy. Conservation of energy is the principle that energy cannot be created or destroyed, only transferred or converted from one form to another. In the case of the swinging ball, the potential energy at the top of the circle is converted into kinetic energy as the ball swings down, and this process repeats as the ball continues to swing. The total energy (potential + kinetic) is therefore conserved throughout the motion of the ball.

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