# Energy in a Spring-Mass System - Help

• tgoodspe
In summary, the conversation is about calculating the maximum stretch in a horizontal spring-mass system with low friction, spring stiffness of 235 N/m, and mass of 0.3 kg. The system is released with an initial compression of 7 cm and an initial speed of 3 m/s. The speaker attempted to use the Energy Principle to find the maximum stretch, but got an incorrect answer. They are questioning if their initial equation is correct and considering converting the initial compression from 7 cm to meters.
tgoodspe
Energy in a Spring-Mass System - Help! :)

1.A horizontal spring-mass system has low friction, spring stiffness 235 N/m, and mass 0.3 kg. The system is released with an initial compression of the spring of 7 cm and an initial speed of the mass of 3 m/s.

(a). What is the maximum stretch during the motion?

## The Attempt at a Solution

So I tried using the Energy Principle to find the maximum stretch;

Kf + Uf = Ki + Ui + W

Kf = 0
W= 0 (I think right because there's no outside force?)

SO: 0 + (.5)(ks)(s^2)final = (.5)mv^2 + (.5)(ks)(s^2)initial

By plugging in variables I got that;
(.5)(ks)(s^2)final = 5758.85 J

(s)final = SQRT(2(5758.85)/(235N)) = 7m

(s)final = 7m

This isn't the right answer, which also sort of makes sense because the stretch shouldn't be the same as the compression. Which makes me think that my initial equation is flip flopped or something of the sorts.

Your energy looks too large. Did you convert the 7cm to meters?

Going to try that now.

## 1. What is a spring-mass system?

A spring-mass system is a physical system that consists of a mass attached to a spring, which is then attached to a fixed point. When the mass is displaced from its equilibrium position, the spring exerts a restoring force that causes the mass to oscillate back and forth around the equilibrium point.

## 2. How does energy play a role in a spring-mass system?

Energy is constantly exchanged between potential energy, stored in the spring, and kinetic energy, possessed by the moving mass, in a spring-mass system. As the mass oscillates, the potential and kinetic energy are constantly being converted back and forth.

## 3. What is the equation for calculating the potential energy of a spring-mass system?

The equation for potential energy in a spring-mass system is U = 1/2 * k * x^2, where k is the spring constant and x is the displacement from the equilibrium position.

## 4. How is the spring constant determined in a spring-mass system?

The spring constant, k, is a measure of the stiffness of the spring and is determined by the physical characteristics of the spring, such as its material and dimensions. It can be calculated by dividing the force applied to the spring by the resulting displacement.

## 5. What factors affect the energy of a spring-mass system?

The energy of a spring-mass system is affected by the mass of the object attached to the spring, the spring constant, and the amplitude of the oscillations. Additionally, external forces such as friction can also affect the energy of the system.

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