Elastic string. Ball. Kinetic energy. Confusion.

[swong1]

Homework Statement

An elastic string with modulus of elasticity=12. Natural length= 0.5m. Mass of ball attached to the end of the string=0.5kg. The other end of the string is fixed at point P. The particle is pulled down until it is 1.5m below P.

Find the kinetic energy of the particle when it is 0.5m above P.

The Attempt at a Solution

The previous question asked me to prove the KE when the string was slack and I got 7.1J, I'm not sure if that is of any relevance when working out this question.

I'm confused as to what the extention is when working out the EPE or if there even is one. Any help will be greatly appreciated!

 

[grzz]

At 0.5m above P there is no elastic PE.

 

[swong1]

Thank you for replying!

How come there is no EPE? Isn't some needed to get it back to its original shape?

 

[grzz]

I am assuming that EPE means elastic potential energy. But EPE is directly proportional to the extension in the string. But since the natural length of the string is 0.5m, then at 0.5m above P the string is not extended and hence has no EPE. Of course the mass has KE and grav PE both of which are the result of the original EPE when at the lowest point.

 

[rwisz]

As a scientist, it is important to always clarify and define the variables and concepts involved in a problem. In this case, we are dealing with an elastic string with a modulus of elasticity of 12, a natural length of 0.5m, and a mass of 0.5kg attached to the end. The other end of the string is fixed at point P.

To find the kinetic energy of the particle when it is 0.5m above P, we need to consider the potential energy stored in the string due to its extension. The extension of the string can be calculated using Hooke's Law, which states that the force applied to an elastic material is directly proportional to the extension of the material.

In this case, the particle is pulled down until it is 1.5m below P, which means the string has been extended by 1m (1.5m - 0.5m). Using Hooke's Law, we can calculate the force applied to the string, which is equal to the weight of the particle (0.5kg * 9.8m/s^2 = 4.9N).

Now, to calculate the potential energy stored in the string, we can use the formula EPE = 1/2 * k * x^2, where k is the modulus of elasticity and x is the extension of the string. Plugging in the values, we get EPE = 1/2 * 12 * (1m)^2 = 6J.

Since the kinetic energy of a particle is equal to its mass multiplied by its velocity squared (KE = 1/2 * m * v^2), we can use the conservation of energy principle to find the kinetic energy of the particle when it is 0.5m above P. Since the potential energy stored in the string is now 6J, the kinetic energy of the particle must also be 6J in order for energy to be conserved.

Therefore, the kinetic energy of the particle when it is 0.5m above P is 6J. It is important to note that this calculation assumes that there is no loss of energy due to friction or other external forces. If these factors are present, the calculated kinetic energy may differ.