Conservation of Energy- Circular Motion Problem

In summary, the total energy of the ball swinging in a vertical circle is equal to the sum of its kinetic and potential energies. To find the total energy, the height of the ball at the top of the circle can be found by multiplying the length of the thread by two, and adding the height of the bottom point of the circle to the floor. For the speed of the ball at the bottom point of the circle, the potential energy at the bottom can be calculated and subtracted from the total energy. The resulting energy can then be used to solve for the speed using the kinetic energy equation.
  • #1
thaixicedxtea
12
0

Homework Statement


A .10 kg solid rubber ball is attached to the end of a .80 m length of light thread. The ball is swung in a vertical circle. Point P, the lowest point of the circle, is .20 m above the floor. The speed of the ball at the top of the circle is 6.0 m/s, and the total energy of the ball is kept constant.

a) Determine the total energy of the ball, using the floor as the zero point for gravitational potential energy.

b) Determine the speed of the ball at point P, the lowest point of the circle.



Homework Equations



1/2mv^2 = KE
mgh = PE
E1=E2


3. The attempt for a solution

I'm thinking for part A, that I'd use the mgh=PE equation. But I also notice that the ball is moving! Would it be KE + PE = TE? I really figured that, but I could be wrong.

For part B, I just know that energy at the top has to equal it at the bottom. I don't know where to go from that.
 
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  • #2
a) The speed of the ball at the top is given. As you have already figured out at the top TE = PE + KE. You have v, find KE. Can, you find h, for PE = mgh, at the top? Remember, that the floor has to be taken as the zero.

b) From part a), you have the TE. Calculate PE at the bottom, and then find KE = TE - PE.
 
  • #3
Oh, now I understand... so the height would be the length times two since the length is considered the radius of the circle, right? Height would be the length times two for the full round top to bottom. Plus the height from the ground to the lowest point of the circle, P, because the floor is the reference point.

For part B, just to be sure, I'll have to solve for v in the KE equation, correct?
 
  • #4
thaixicedxtea said:
Oh, now I understand... so the height would be the length times two since the length is considered the radius of the circle, right? Height would be the length times two for the full round top to bottom. Plus the height from the ground to the lowest point of the circle, P, because the floor is the reference point.

For part B, just to be sure, I'll have to solve for v in the KE equation, correct?


yes...you are right..and right again for part B. :)
 

What is the conservation of energy?

The conservation of energy is a fundamental principle in physics that states energy cannot be created or destroyed, but can only be transferred or transformed from one form to another. In other words, the total energy in a closed system remains constant.

How does the conservation of energy apply to circular motion?

In circular motion, the conservation of energy states that the total mechanical energy of an object, which is the sum of its kinetic energy and potential energy, remains constant as long as there is no external work or non-conservative forces acting on the object.

What are the key factors to consider when solving a conservation of energy- circular motion problem?

The key factors to consider include the mass of the object, the velocity of the object, the radius of the circular path, and any external forces acting on the object. It is also important to identify any changes in potential or kinetic energy throughout the motion.

How can energy be conserved in a circular motion problem?

Energy can be conserved in a circular motion problem by ensuring that the total mechanical energy remains constant throughout the motion. This can be achieved by accounting for all forms of energy, such as kinetic, potential, and thermal energy, and any external forces or work done on the object.

What are some real-world applications of the conservation of energy in circular motion?

The conservation of energy in circular motion has many practical applications, such as in amusement park rides, satellite orbits, and planetary motion. It is also essential for understanding the behavior of objects in circular motion, such as roller coasters, carousels, and Ferris wheels.

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