# Conservation of Mechanical Energy

• sunny17
In summary, the conversation discusses finding the change in kinetic energy and potential energy, determining if the system is conservative, and calculating the energy lost to friction and coefficient of friction for a block of mass m moving at a certain velocity and compressing a spring by distance x. The equations used are KE = 1/2mv^2 and PE of Spring = 1/2kx^2. The approach described seems correct, with the only confusion being whether to report energy as negative or positive. It is equivalent to say there was a loss of 20J or a change of -20J, and similarly for the work done by friction.
sunny17

## Homework Statement

This is my first time posting here guys so correct me if I am wrong. This question was on my test and I wanted to know if I did it right. There is a block of mass m and it is moving at a certain velocity before pressing against a spring which compresses distance x.

Find Change in Kinetic Energy
Change in Potential Energy
Is this a conservative energy. Why?
Energy lost to Friction
Coefficent of Friction.

## Homework Equations

KE = 1/2mv^2
PE of Spring = 1/2kx^2

## The Attempt at a Solution

I don't know the exact measurements for the variables but I used the kinetic energy formula to find intial KE and the final should be 0 because it turns into Potential correct? I got negative for that.

I found change in potential by setting intial to 0 and using the equation.

I then noticed that kinetic and potential weren't equal and potential was smaller so there was no conservation of energy.

The loss in energy is friction? I then used this to find the coefficent. Is this correct?

Welcome to Physics Forums.

The approach you describe sounds right, although it's difficult to say for sure without seeing exactly what you did.

PeroK said:
Welcome to Physics Forums.

The approach you describe sounds right, although it's difficult to say for sure without seeing exactly what you did.

Energy cannot be negative correct? I got negative Kinetic Energy but reported it as positive would this be right?

sunny17 said:
Energy cannot be negative correct? I got negative Kinetic Energy but reported it as positive would this be right?

Energy is a bit like money. If you lose it, you could describe that as a negative change.

PeroK said:
Energy is a bit like money. If you lose it, you could describe that as a negative change.

Then say I get Intial KE as 100J and Final is 0 because it converts to PE then Change in KE is -100?
Assuming the PE is 80J.

If I were to find the work done by Friction would it be -100 - 80? = -180J?
I thought it would be 100 - 80 = 20J.

sunny17 said:
Then say I get Intial KE as 100J and Final is 0 because it converts to PE then Change in KE is -100?
Assuming the PE is 80J.

If I were to find the work done by Friction would it be -100 - 80? = -180J?
I thought it would be 100 - 80 = 20J.

It really just like bookkeeping. You start with KE = 100J and end with PE = 80J, so:

1) There is a loss of 20J.
2) The change in energy is -20J.

These are equivalent.

It's then s equally valid to say:

a) The work done by friction is 20J
b) The work done by friction is -20J.

a) assumes you know that friction takes energy out of the system and b) makes this more explicit.

PeroK said:
It really just like bookkeeping. You start with KE = 100J and end with PE = 80J, so:

1) There is a loss of 20J.
2) The change in energy is -20J.

These are equivalent.

It's then s equally valid to say:

a) The work done by friction is 20J
b) The work done by friction is -20J.

a) assumes you know that friction takes energy out of the system and b) makes this more explicit.

Thank You. That makes sense so much more sense now.

## 1. What is conservation of mechanical energy?

The conservation of mechanical energy is a fundamental principle in physics that states that the total amount of mechanical energy in a closed system remains constant over time. This means that energy cannot be created or destroyed, but it can be transformed from one form to another.

## 2. What are the two forms of mechanical energy?

The two forms of mechanical energy are kinetic energy and potential energy. Kinetic energy is the energy of motion, while potential energy is the energy that an object possesses due to its position or configuration.

## 3. How is the conservation of mechanical energy related to the law of conservation of energy?

The conservation of mechanical energy is a specific application of the broader law of conservation of energy, which states that energy cannot be created or destroyed in any physical process. The conservation of mechanical energy specifically applies to systems where only mechanical energy is involved, while the law of conservation of energy applies to all forms of energy.

## 4. Can mechanical energy be converted into other forms of energy?

Yes, according to the law of conservation of energy, mechanical energy can be converted into other forms of energy, such as thermal energy or electrical energy. For example, when an object falls from a height, its potential energy is converted into kinetic energy, and that kinetic energy can then be converted into thermal energy upon impact.

## 5. What are some real-world examples of conservation of mechanical energy?

Some examples of conservation of mechanical energy in everyday life include a pendulum swinging back and forth, a roller coaster going down a track, or a ball bouncing on the ground. In all of these situations, the total amount of mechanical energy remains constant, even as the energy is transformed between kinetic and potential forms.

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