# Energy and Simple Harmonic Motion of block

• Pius
In summary, the conversation discusses the elastic potential energy of a spring/mass system. The initial system has a 3.2-kg block hanging from the end of the spring, resulting in an elastic potential energy of 1.8J. The question asks what the elastic potential energy would be if the 3.2-kg block was replaced with a 5.0-kg block. The formula for elastic potential energy is given, but the extension of the spring (x) is unknown. However, it is determined that the system is stationary, meaning that x is a constant. The net force acting on the block is also discussed. In conclusion, the elastic potential energy of the system when the 3.2-kg

## Homework Statement

A 3.2-kg block is hanging stationary from the end of a vertical spring that is attached to the ceiling. The elastic potential energy of this spring/mass system is 1.8J. What is the elastic potential energy of the system when the 3.2-kg block is replaced by a 5.0-kg block?

## Homework Equations

Elastic potential energy=1/2kx^2
Gravitational potential energy=mgh

## The Attempt at a Solution

The problem is that you have the extension x of the spring in your formula, which you do not know. However, there is an extra clue in the word "stationary". What does that mean?

it is not moving, x=0?

What should I put in for h and k? Thank you, CompuChip!

Exactly, it is not moving. But that does not mean that x = 0 (then the spring would be in its equilibrium position... but it is stretched by the mass that's hanging on it)... it merely says that x is a constant. But what can you say about the net force acting on the block. Which forces are there?

'x' is the extension from the equilibrium point in the spring when the 3.2kg mass is changed to 5kg. Because 'g' and 'k' stay constant it is just simple ratios...

## 1. What is energy in the context of simple harmonic motion of a block?

Energy is the ability to do work or cause change. In the context of simple harmonic motion of a block, it refers to the potential and kinetic energy that is constantly exchanged as the block oscillates back and forth.

## 2. How is energy conserved in simple harmonic motion of a block?

Energy is conserved in simple harmonic motion of a block because the total energy (potential + kinetic) remains constant throughout the oscillations. As the block moves from one extreme to the other, the energy is constantly transferred between potential and kinetic forms, but the total amount remains the same.

## 3. What factors affect the amount of energy in simple harmonic motion of a block?

The amount of energy in simple harmonic motion of a block is affected by the amplitude of the motion, the mass of the block, and the spring constant of the restoring force. As these factors change, the total energy and the ratio of potential to kinetic energy will also change.

## 4. How is the period of oscillation related to energy in simple harmonic motion of a block?

The period of oscillation (the time it takes for the block to complete one full cycle) is not directly related to the energy in simple harmonic motion. However, the period can be affected by the amplitude of the motion, which in turn can affect the amount of energy in the system.

## 5. Can the energy in simple harmonic motion of a block ever reach zero?

No, the energy in simple harmonic motion of a block will not reach zero unless there is an external force acting on the system. In a frictionless environment, the energy will continue to oscillate between potential and kinetic forms without ever reaching zero.