# What is the total distance traveled by the mass on a compressed spring?

• Jinzui
In summary, the problem involves a 10kg mass placed on a horizontal spring with a spring constant of 200N/m that is compressed 80cm. The mass leaves the spring at the equilibrium point with a velocity of 3.23m/s. Using the equation for conservation of energy, the total distance traveled by the mass can be found to be 4.35m. The spring does not need to be considered in the solution, as it is only there to confuse the solver. It is important to carefully read and understand the problem before attempting to solve it.
Jinzui

## Homework Statement

A horizontal k=200N/m spring is compressed 80cm. A 10kg mass is palced at the of of the spring on a u(mew)=0.15 surface. The mass leaves the spring at the equilibrium (x=0) point with 3.23m/s. Find the total distance (starting from rest) traveled by the mass. (Answer= 4.35)

yea i got my other homework questions but this one confused me. The solution is probably simple, but i have the tendency to overthink. Thank you for the help.

## Homework Equations

PEs -umg(0.8) = KE

## The Attempt at a Solution

1/2(200*x2) - (0.15*10*9.8*x)= 1/2 (10*v2)

then i used the quadratic formula to find x, but i got like 0.76 i think.

There is no need to consider the elastic potential energy; the question already tells you that the mass leaves the spring with a certain velocity, hence you can safely ignore the spring from then on.

Yeah, start with when the mass leaves the spring. There is no need to take the spring into consideration. It is just there to confuse you. When it comes to these problems, it's best not to over think them other wise you can get overwhelmed easily if you're just starting out. Spend time reading the problem rather than solving. Good Luck.

## 1. What is potential energy?

Potential energy is a form of energy that an object possesses due to its position or condition. It is the energy that an object has the potential to convert into other forms of energy, such as kinetic energy.

## 2. How is potential energy related to springs?

Potential energy is related to springs through Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed from its equilibrium position. This means that the further a spring is stretched or compressed, the greater its potential energy becomes.

## 3. What is the formula for calculating potential energy?

The formula for calculating potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above a reference point. This formula is often used for objects in a gravitational field, but for springs, the formula is PE = 1/2kx^2, where k is the spring constant and x is the displacement from the equilibrium position.

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

Yes, potential energy can be converted into other forms of energy. For example, when a spring is released, its potential energy is converted into kinetic energy as it begins to vibrate or move. Similarly, when an object falls from a height, its potential energy is converted into kinetic energy as it accelerates towards the ground.

## 5. How is potential energy important in everyday life?

Potential energy plays a crucial role in our everyday lives. It is the energy that allows us to lift objects, run, and even move our fingers to type. It is also used in various technologies, such as hydroelectric power plants and wind turbines, where potential energy is converted into electrical energy. Understanding potential energy also helps us to understand the behavior of objects in different situations, allowing us to make more informed decisions and inventions.

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