Question regarding Elastic Potential Energy

In summary, the question asks about the distance a particle P will move when it is projected downwards from a hanging position. The particle is attached to a light elastic string of natural length l, with the other end attached to a ceiling at point A. When P is in equilibrium, the length of the string is 5/3l. The question wants to prove that if P is projected downwards from A with a specific speed, it will come to rest after moving a distance of 10l/3. The confusion lies in whether the distance includes the natural length of the string or not. The answer is yes, as the question specifies that the particle is projected from A, the point where the string is attached.
  • #1
garyljc
103
0
Hey guys ,
I got another question , here goes :

A particle P of mass m is attached to one end of a light elastic string of natural length l whose other end is atached to a point A on a ceiling. When P hangs in equilibrium AP has legth 5/3l. Show that if P is projected vertically downwards from A with speed *squareroot*3gl/2 , P will first come to instantaneous rest after moving a distance of 10l/3 .

What confuses me , is the distance moved . Does it include the natural length or not ? Please show me the proof :biggrin: ... Geeez ... thanks :shy:
 
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  • #2
hmmm ... no one ? I just need to know does the distance includes the natural length =) Can anyone tell me please ?
 
  • #3
garyljc said:
Hey guys ,
I got another question , here goes :

A particle P of mass m is attached to one end of a light elastic string of natural length l whose other end is atached to a point A on a ceiling. When P hangs in equilibrium AP has legth 5/3l. Show that if P is projected vertically downwards from A with speed *squareroot*3gl/2 , P will first come to instantaneous rest after moving a distance of 10l/3 .

What confuses me , is the distance moved . Does it include the natural length or not ? Please show me the proof :biggrin: ... Geeez ... thanks :shy:
The question says that it is projected vertically from A which is the point where the string is attached. So the distance includes the length at rest of the string.
 
  • #4
ahhh , got it ... I'm confuse before that lol . thanks = )
 

1. What is elastic potential energy?

Elastic potential energy is the potential energy stored in an object when it is stretched or compressed. This energy is stored in the elastic materials such as rubber bands, springs, or bungee cords.

2. How is elastic potential energy calculated?

Elastic potential energy is calculated using the formula E = 1/2kx^2, where E is the elastic potential energy, k is the spring constant, and x is the displacement of the object from its equilibrium position.

3. What factors affect the amount of elastic potential energy in a system?

The amount of elastic potential energy in a system is affected by two main factors: the spring constant and the displacement of the object from its equilibrium position. A higher spring constant and a larger displacement will result in a higher amount of elastic potential energy.

4. How is elastic potential energy related to work?

Elastic potential energy is related to work through the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. This means that when an object is stretched or compressed, work is done on it, and this work is stored as elastic potential energy.

5. What are some real-life examples of elastic potential energy?

Some common examples of elastic potential energy include a stretched rubber band, a compressed spring, and a bungee cord before it is released. Other examples include a trampoline, a diving board, and a catapult.

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