Pendulums with Mechanical Energy (conical pendulum?)

In summary, the question is asking how high the pendulum bob must be raised before being released in order to maintain a taut string and circular motion around the rod. The solution involves considering the conversion of kinetic energy into gravitational potential energy and the use of equations such as Potential Energy = mgh and Kinetic Energy = 1/2mv^2. The distance from the rod to the pendulum bob is also a factor in determining the necessary height. Overall, this problem is similar to a conical pendulum and further questions can be directed to the source provided.
  • #1
victoration1
7
0

Homework Statement



The pendulum bob in Figure 6.11 must circle
the rod interrupting its swing, and the string
must remain taut at the top of the swing. How
far up must the bob be raised before releasing
it to accomplish these goals?

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Homework Equations



Potential Energy = mgh
Kinetic Energy = 1/2mv^2
mgh = 1/2mv^2

The Attempt at a Solution



I'm still unclear with what the question is asking for or how I'm suppose to solve it; though I'm guessing it deals with the conversion of kinetic energy into gravitational potential energy and maximum height. How the rod play into the question, or what the distance from the rod to the pendulum bob means, I've no idea. This sounds awfully similar to a conical pendulum, which a quick wikipedia search showed as pretty complicated.
So, how do?
 
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  • #2
When the string hits the rod, it the bob will start circling the rod in a 10 cm radius circle. It won't reach the point 10 cm above the rod unless you release it from high enough. How high is 'high enough'?
 
  • #3
Here is the Solution for you: Please click on the image. For more questions please send requests here...
 

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FAQ: Pendulums with Mechanical Energy (conical pendulum?)

What is a pendulum with mechanical energy?

A pendulum with mechanical energy refers to a type of pendulum that uses the principle of potential and kinetic energy to oscillate back and forth. It typically consists of a mass attached to a string or rod that is suspended from a fixed point, allowing it to swing freely.

How does a conical pendulum work?

A conical pendulum works by utilizing the forces of gravity and tension to keep the pendulum in motion. As the pendulum swings, the tension in the string or rod changes, causing the pendulum to accelerate towards the center of the circular path. This creates a circular motion, resulting in a conical swing.

What factors affect the period of a pendulum with mechanical energy?

The period of a pendulum with mechanical energy is affected by the length of the string or rod, the mass of the pendulum, and the acceleration due to gravity. The longer the string, the slower the period, while a heavier mass and higher acceleration due to gravity will result in a faster period.

How is energy conserved in a pendulum with mechanical energy?

In a pendulum with mechanical energy, the potential energy is converted to kinetic energy as the pendulum swings back and forth. At the highest point of the swing, the potential energy is at its maximum, while at the lowest point, the kinetic energy is at its maximum. This conversion of energy allows the pendulum to continue oscillating without losing energy.

What are some real-life applications of a conical pendulum?

A conical pendulum has various real-life applications, such as in amusement park rides, clock mechanisms, and seismometers to measure earthquakes. It is also used in sports equipment, such as a swinging baseball bat or a tennis racquet, to increase the speed and power of the swing.

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