Calculating Potential Energy Increase in a Massless Spring

In summary, potential energy increase refers to a change in potential energy due to an external force or change in position. Some common examples include stretching a spring, lifting an object against gravity, and compressing a gas in a container. The calculation for potential energy increase varies depending on the type of potential energy involved, such as gravitational or elastic. Potential energy increase is closely related to kinetic energy, as they are both forms of energy and can be converted into each other. In theory, potential energy can increase indefinitely, but in reality, there are limitations such as material strength and the effects of gravity.
  • #1
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Homework Statement


A massless spring hangs from the ceiling. How much does its potential energy increase, if a 28.8 kg mass is attached to it? The spring constant is 4800 N/m.




The Attempt at a Solution



I set 0.5Kx^2=mg. I then divided the spring constant by mg. I got 17 J. This really doesn't seem right to me. Any import would be greatly appreciated
 
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  • #2
-kx = mg

not 0.5kx^2=mg

find x and then proceed
 
  • #3
Ok so I solved for x and got 0.0588 meters. I then plugged it into the 0.5kx^2 and got 8.3 J. Does this seem correct?
 

FAQ: Calculating Potential Energy Increase in a Massless Spring

What is potential energy increase?

Potential energy increase refers to the change in potential energy of an object or system due to some external force or change in position.

What are some examples of potential energy increase?

Some common examples of potential energy increase include stretching a spring, lifting an object against gravity, and compressing a gas in a container.

How is potential energy increase calculated?

The calculation for potential energy increase depends on the specific type of potential energy involved. For gravitational potential energy, it is calculated using the formula U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance above the ground. For elastic potential energy, it is calculated using U = 1/2kx^2, where k is the spring constant and x is the displacement from the equilibrium position.

What is the relationship between potential energy increase and kinetic energy?

Potential energy increase is closely related to kinetic energy, as they are both forms of energy. When an object experiences a potential energy increase, it usually means that it is moving to a higher position, which often results in a decrease in kinetic energy. However, the total energy of the object remains constant, as potential energy is converted into kinetic energy and vice versa.

Can potential energy increase indefinitely?

In theory, yes, potential energy can increase indefinitely as long as an external force is continuously applied. However, in reality, there are limitations such as the maximum strength of materials and the effects of gravity, which prevent potential energy from increasing infinitely.

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