Changes in Mechanical Energy for Nonconservative Forces

In summary, the conversation revolves around a softball pitcher swinging a ball and releasing it at the bottom of a circular path. The question is asked about the speed of the ball upon release and how to calculate it using kinetic energy, potential energy, and work. After some discussion, it is determined that the work done on the ball is not 0 and the correct method for solving the problem is using energy methods. The final answer is calculated to be 26.5 m/s with the help of a small correction in the calculation of work.
  • #1
Bri
20
0
I have a problem for the subject in the title. I'm not really sure where to start, and I can't figure it out.

In her hand a softball pitcher swings a ball of mass .250 kg around a vertical circular path of radius 60.0 cm before releasing it from her hand. The pitcher maintains a component of force on the ball of constant magnitude 30.0 N in the direction of motion around the complete path. The speed of the ball at the top of the circle is 15.0 m/s. If she releases the ball at the bottom of the circle, what is its speed upon release?

If someone could point me in the right direction here...
Thanks.
 
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  • #2
How much work does she do on the ball? (So what happens to the total mechanical energy?)
 
  • #3
Wouldn't the work she does be 0? Since it goes in a circle and ends up back at the starting position?
 
  • #4
It's a rotational kinematics question. First, with the info given, you can work out angular acceleration, initial angular speed and the angular displacement. After that, just plug them into the most familiar equation in kinematics question to find the final angular speed, which then allow you to find its tangential speed.
 
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  • #5
Bri said:
Wouldn't the work she does be 0? Since it goes in a circle and ends up back at the starting position?
No. That reasoning would apply to a conservative force, but the force of her hand on the ball is not a conservative force.

In any case, she applies a force over a distance, so work is done.
 
  • #6
I don't think I know any of that angular stuff you posted about...
We're supposed to be using Kinetic Energy, Potential Energy, Work, etc. to find the answer.
 
  • #7
Bri said:
I don't think I know any of that angular stuff you posted about...
We're supposed to be using Kinetic Energy, Potential Energy, Work, etc. to find the answer.
Using energy methods is the easy way to do this problem.
 
  • #8
Ok, so work would be 30 * 2pi*.6 = 113.1
I'm still not sure what to do...
I tried
KE(initial) + U(initial) + W(external) = KE(final) + U(final)
.5(.25)(15)^2 + 9.8(.25)(1.2) + 113.1 = .5(.25)v^2 + 9.8(.25)(0)
I solved for v and got 34 m/s, which according to my book is wrong (should be 26.5 m/s)
 
  • #9
Bri said:
Ok, so work would be 30 * 2pi*.6 = 113.1
I'm still not sure what to do...
I tried
KE(initial) + U(initial) + W(external) = KE(final) + U(final)
.5(.25)(15)^2 + 9.8(.25)(1.2) + 113.1 = .5(.25)v^2 + 9.8(.25)(0)
I solved for v and got 34 m/s, which according to my book is wrong (should be 26.5 m/s)
Your method is fine, but you made a mistake in calculating the work. The work is done over half the circle, not the whole. (Since you are given the speed at the top of the circle.)
 
  • #10
Oh, ok!
Thanks so much for the help!
 
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1. What is mechanical energy?

Mechanical energy is the energy possessed by an object due to its motion or position. It is the sum of an object's kinetic energy (energy of motion) and potential energy (energy stored in its position or configuration).

2. What are nonconservative forces?

Nonconservative forces are external forces that do work on an object and cause a change in its mechanical energy. Unlike conservative forces, the work done by nonconservative forces depends on the path taken by the object and does not result in a net energy gain or loss.

3. How do nonconservative forces affect mechanical energy?

Nonconservative forces can either increase or decrease an object's mechanical energy, depending on the direction of the force and the motion of the object. If the force is in the same direction as the object's motion, it will add energy to the object. If the force is in the opposite direction, it will remove energy from the object.

4. What is the equation for calculating changes in mechanical energy for nonconservative forces?

The equation for calculating changes in mechanical energy for nonconservative forces is ∆E = Wnc, where ∆E is the change in mechanical energy and Wnc is the work done by nonconservative forces.

5. How do nonconservative forces affect the conservation of mechanical energy?

Nonconservative forces violate the principle of conservation of mechanical energy, as they can cause a change in an object's mechanical energy. This is because the work done by nonconservative forces is not reversible, and some of the object's energy is lost to the surroundings as heat or sound.

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