Conservation of Energy of an Interrupted Pendulum

In summary: It states that the total energy of a system remains constant, and can be expressed as the sum of kinetic and potential energies. The Interrupted Pendulum apparatus shown in (Figure 1) is used to explore this concept. A ball, attached to a horizontal cord of length L, is released from rest when the string is horizontal and follows a dashed trajectory similar to a pendulum. The ball then follows a tighter circular trajectory when interrupted by a peg located at a distance d directly below the fixed end of the cord. The conversation then focuses on finding the speed of the ball at the top of the circular path (in terms of L and g) when d = 0.75L, determining the minimum distance d_min (expressed as a
  • #1
The studio explores the conservation of energy using the Interrupted Pendulum apparatus shown in (Figure 1). A ball is attached to a horizontal cord of length L whose other end is fixed. A peg is located at a distance d directly below the fixed end of the cord. The ball is released from rest when the string is horizontal, as shown in the figure, and follows the dashed trajectory in a fashion similar to a pendulum until the peg interrupts it, which causes the ball to suddenly follow a tighter circular trajectory.

Image: http://session.masteringphysics.com/problemAsset/1000232220/3/peg.jpg

1) If d = 0.75L, find the speed of the ball when it reaches the top of the circular path about the peg, in terms of L and g.

2) What is the minimum distance d_min (expressed as a fraction of L) such that the ball will be able to make a complete circle around the peg after the string catches on the peg? (Hint: what speed does the ball need to have at the top of its arc if it is to just barely continue to move in a circle?)

3) Will the ball be able to make a complete circle about the peg if d = 0.5L?

Attempt at solving the equation:

I'm not sure where to start, but I thought about using d=V_0*sqrt(m/k). Any explanations would be great! Thanks!
 
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  • #2
Have you tried starting with the conservation of energy?
 

1. What is the concept of Conservation of Energy?

The concept of Conservation of Energy states that energy cannot be created or destroyed, but it can be transferred from one form to another. In the case of an interrupted pendulum, the potential energy of the pendulum is converted into kinetic energy as it swings back and forth.

2. How does an interrupted pendulum demonstrate Conservation of Energy?

An interrupted pendulum demonstrates Conservation of Energy because the potential energy of the pendulum at its highest point is equal to the kinetic energy at its lowest point. As the pendulum swings back and forth, the energy is constantly being transferred between potential and kinetic forms, but the total amount of energy remains constant.

3. What factors affect the Conservation of Energy in an interrupted pendulum?

The main factors that affect the Conservation of Energy in an interrupted pendulum are the length of the pendulum, the mass of the bob, and the initial angle at which the pendulum is released. These factors impact the potential and kinetic energies of the pendulum and determine how much energy is transferred between the two forms.

4. Can the Conservation of Energy be violated in an interrupted pendulum?

No, the Conservation of Energy cannot be violated in an interrupted pendulum. As long as there is no external force acting on the pendulum, the total amount of energy will remain constant. However, some energy may be lost due to friction or air resistance, which may cause the pendulum to eventually come to a stop.

5. How is the Conservation of Energy of an interrupted pendulum useful in real-world applications?

The Conservation of Energy is used in real-world applications such as energy conversion and conservation. For example, the concept is applied in energy-efficient buildings to minimize energy loss and maximize the use of renewable energy sources. It is also used in the design of roller coasters and other amusement park rides to ensure the safety and efficiency of the ride.

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