# Calculating spring constant

• Ajeezy
In summary, we have a 1 kg mass hung from a spring and given initial and final velocities, as well as initial and final heights. To calculate the spring constant, we use the conservation of energy equation with the potential elastic factored in. However, to account for the negative initial and final heights, we must first determine the initial and final displacements of the spring under the static load. By plugging these values into the given equation and solving for the spring constant, the correct answer can be obtained.

## Homework Statement

A mass 1 kg mass is hung from a spring.
Calculate the spring constant from the given data. Velocity initial= 3.0 m/s Velocity final= 1.5 m/s. The initial height traveled is 0.1 meters and the final is 0.25 meters. These height values will be negative since i picked my starting point at the origin so they have moved below the X making them negative.

## Homework Equations

I know i am supposed to use the conservation of energy equation with the potential elastic factored into the total PE. the equation would be (1/2*m*v^2)+(mgh)+1/2*k*x^2)=(1/2*m*v^2)+(mgh)+1/2*k*x^2) where the left is the initial and the right is the final. However i keep getting the wrong answer. I think I am doing a simple algebraic error in my calculations. any guidance is appreciated

## The Attempt at a Solution

I think you have to determine the initial displacement of the spring under the static load:

Xo = mg / K

Then final displacement is:

Xf = mg / K - $$\Delta$$X

Where $$\Delta$$X = 0.25m - 0.1m = 0.15m

Put that in your equation and do the transformations and it should give you the correct answer.

## What is a spring constant?

A spring constant is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

## How do you calculate the spring constant?

The spring constant can be calculated by dividing the applied force by the resulting displacement of the spring. This can be represented by the equation k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

## What units is the spring constant measured in?

The spring constant is typically measured in units of force per unit of displacement, such as N/m (newtons per meter) or lbs/in (pounds per inch).

## How does the spring constant affect the behavior of a spring?

The spring constant determines the level of resistance a spring will have to stretching or compressing. A higher spring constant means the spring is stiffer and will require more force to stretch or compress, while a lower spring constant indicates a more flexible spring.

## Can the spring constant change?

Yes, the spring constant can change depending on factors such as the material, length, and diameter of the spring. It can also change if the spring is stretched beyond its elastic limit, causing the spring to permanently deform and alter its spring constant.
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