# Lab Homework 2

Name: ________________________________ _____________________ Date:_____________

## Hooke’s Law & Springs

### Introduction

Hooke’s Law teaches us how springs can store and use potential energy. It is expressed as a ratio of the force needed to stretch a spring and the distance it is stretched: Where “k” is the spring’s constant, a value that is the same for the spring no matter how much force is acting on it; “F” is the force used to displace the spring, and “x” is the distance the spring is displaced, in meters. The units for spring constant are N/m.

In this simulation lab, you will calculate the spring constants of three different springs, one with a low spring constant, one with a medium spring constant, and one with a large spring constant. You will then use those spring constants to find the mass of three unknown weights.

### Steps

1. Click the simulation. You may use the “Intro” simulation for the measurements. Spend some time playing with the springs and seeing how they work. Clicking “Natural Length”, “Equilibrium Position” and using the ruler (the light yellow color ruler and the timer can be found in the lower gray box) can help you measure the displacement of the spring.

2. When you are ready to begin the lab, turn on the “Natural Length”, “Equilibrium Position” and use the ruler. Start with 50 grams (0.05 kg) and the Spring Constant slid all the way down to small. Use this and your Weight formula (w = mg) to find the force pulling on the spring, and measure how many meters the spring is displaced. Click the Stop Sign at the top to get it to stop oscillating. Remember, divide by 100 to convert cm to m! Add this to your data table below, and use these values to calculate the spring constant. Repeat with 100 g (0.1 kg) and 250g (0.25 kg), and find the average of all the spring constants that you calculated. (g = 9.8 m/s2)

### Spring Constant set to Small

 Mass (kg) Gravity (g) Force (N) Displacement (m) Spring Constant (N/m) 0.05 kg 0.1 kg 0.25 kg Average:

3. Repeat the lab with the spring constant set halfway between “Small” and “Large”.

### Spring Constant Set Halfway between Small and Large

 Mass (kg) Gravity (g) Force (N) Displacement (m) Spring Constant (N/m) 0.05 kg 0.1 kg 0.25 kg Average:

4. And repeat once more with the Spring Constant set all the way up to “Large”

### Spring Constant Set at Large

 Mass (kg) Gravity (g) Force (N) Displacement (m) Spring Constant (N/m) 0.05 kg 0.1 kg 0.25 kg Average:

5. Now we’ll find the mass of the three “Mystery Weights” That are provided. Since we now know the spring constant (the average) we can work backwards to find the mass. Rearranging Hooke’s Law, we have:

And using the weight in place of force, we get:

So we’ll multiply the spring constant you found above by the displacement, then divide that by gravity to get the mass of our “mystery masses”. Use the three spring constants (the averages) to fill in the data table below, being careful to use meters and kilograms.

Mass color: Pink:

 Spring Constant (N/m) Displacement (m) Weight (N) Gravity (g) Mass (kg)

Mass color: Green:

 Spring Constant (N/m) Displacement (m) Weight (N) Gravity (g) Mass (kg)

Mass color: Orange:

 Spring Constant (N/m) Displacement (m) Weight (N) Gravity (g) Mass (kg)

6. Select the words that best fill in the conclusion:

“The larger the Spring Constant, the (Stiffer/ Looser) the spring, and the (More/Less) force is required to get it to be displaced.”

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