# Why am I getting a negative? (Energy conservation)

• jegues
In summary, the block has an initial kinetic energy of 1.68 J and is sliding on a rough table. Just before it hits the spring, the friction energy must be subtracted from the energy conservation equation. Solving the quadratic equation, the negative solution is unphysical and the positive solution is the distance the spring is compressed. It is important to remember that thermal energy is always on the initial side of the energy conservation equation and it will always be negative.
jegues
Why am I getting a negative!? (Energy conservation)

## Homework Statement

2kg block slides on a rough table with uk = 0.3, just before the block hits the spring V0 = 1.3 m/s. k = 120N/m. How far is the spring compressed?

## Homework Equations

Ki + Us = Kf + Us - Eth

## The Attempt at a Solution

Okay just before it touches the spring, what energy does it have?

Ki = 1/2(2)(1.3)^2 = 1.68 J

1.68J + 0 = 0 + 1/2kx^2 -fx
0 = 1/2kx^2-mgukx-1.68
0 = 60x^2 -5.88x - 1.68
x= 0.22 or x= -0.13

Why is my answer negative!?

The only thing i can think of that intially the spring is not compressed. (x=0) Once you compress the spring, the spring must get smaller, what's smaller than 0? -0.13

Can anyone clearly explain to me why this is negative!?

Bump, exams tomorrow hoping for an answer ASAP!

Ki + Us = Kf + Us - Eth

Should be Ki + Us = Kf + Us + Eth.

Initial kinetic energy of the block, plus initial potential energy of the spring, equals: final kinetic energy of the block, plus final potential energy of the spring, plus energy expended to friction.

Then you solve the quadratic equation and you get two solutions, the negative solution is unphysical, the positive solution is your answer.

Oh I thought of it this way,

I start with a kinetic energy, and all of this energy is going to be converted into to spring energy, BUT there's friction, so just take away the energy friction consumes.

Is this wrong?

jegues said:
Oh I thought of it this way,

I start with a kinetic energy, and all of this energy is going to be converted into to spring energy, BUT there's friction, so just take away the energy friction consumes.

Is this wrong?

Then you have to put the friction term on the left, with the '-' in front of it.

Thats correct, hopefully I can fix this understanding in my head before tomorrow :S.

Any tips how to think/understand this better?

Could it be as simple as saying, regardless of the circumstances of the problem my thermal energy is always going to be on the INITIAL side of my equation(for energy conservation) and it will always be NEGATIVE?

Could it be as simple as saying, regardless of the circumstances of the problem my thermal energy is always going to be on the INITIAL side of my equation(for energy conservation) and it will always be NEGATIVE?

Bump anyone know if what I stated above is correct?

lol i was stuck in the same question as well but its kinda easy
and don't break ur head with this stuff.. just remember the equation u won't have time to think about it on the exam

## 1. Why am I getting a negative result when trying to conserve energy?

There are a few reasons why you may be getting a negative result when trying to conserve energy. One possible explanation is that your conservation method may not be effective or efficient enough to make a noticeable difference in your energy usage. Another reason could be that there are other factors, such as old or faulty appliances, that are contributing to your high energy consumption.

## 2. Can negative results from energy conservation efforts be reversed?

Yes, negative results from energy conservation efforts can be reversed. It may require some adjustments to your conservation methods or identifying and addressing any underlying issues that are causing high energy usage. With persistence and dedication, it is possible to achieve positive results in energy conservation.

## 3. Is it normal to see a negative impact on my energy bill when trying to conserve energy?

It is not uncommon to see a slight increase in your energy bill when first starting to conserve energy. This could be due to the initial cost of purchasing energy-efficient appliances or making home improvements. However, in the long run, energy conservation efforts should result in lower energy bills.

## 4. What are some common mistakes that can lead to negative results in energy conservation?

Some common mistakes that can lead to negative results in energy conservation include not properly maintaining appliances, using outdated or inefficient technology, and not taking advantage of natural lighting and ventilation in your home. It is also important to be mindful of your daily habits and make small changes that can add up to significant energy savings.

## 5. How can I accurately measure the effectiveness of my energy conservation efforts?

The best way to measure the effectiveness of your energy conservation efforts is by tracking your energy usage and comparing it to previous months or years. Many energy companies offer tools or apps that allow you to monitor your energy consumption in real-time. You can also conduct an energy audit to identify areas where you can make improvements and measure the impact of those changes over time.

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