Please answer all the questions ### Hooke's Law and Spring MechanicsRobert Hooke discovered a proportionality between the force $ F $ applied to a spring and the distance $ x $ it stretches (or compresses). The equation is generally written:\[ F = kx \]where the constant of proportionality $ k $ is known as the **spring constant** — a measure of the stiffness of the spring.Experimentally, it is much easier to vary the force on a spring and measure its change in length than vice versa, so the equation as tested here becomes:\[ x = \left( \frac{1}{k} \right) F \hspace{10mm} (1) \]The experimental setup is shown below. [Include a diagram if possible]A spring is suspended vertically with a mass hanger attached to its lower end. Mass is added to the hanger, thus increasing the force on the spring (remember that weight is a force). A meter stick is used to measure the resulting distance stretched.#### Detailed Procedure:1. **Setup**: Attach a spring to a fixed stand. Hang a mass hanger from the spring’s lower end.2. **Measurement**: Use a meter stick to measure the initial length of the spring.3. **Increasing Force**: Incrementally add known masses to the hanger. For each mass added, record the new length of the spring.4. **Data Analysis**: Calculate the force applied for each mass using $ F = mg $ (where $ m $ is the mass added and $ g $ is the acceleration due to gravity). Measure the extension $ x $ (difference between initial and new lengths).5. **Verification of Hooke’s Law**: Plot $ F $ vs. $ x $. A linear relationship verifies Hooke’s Law, and the slope of the line gives the spring constant $ k $.This experiment illustrates the practical application of Hooke's Law and aids in understanding the relationship between force, spring constant, and displacement in spring mechanics. # Relationship Between Force and Distance## Problem Set1. **What is the relationship you are testing between force and distance?** In this question, you need to determine the specific relationship being tested between the force applied to an object and the distance over which it acts.2. **A graph of what vs. what would be required to confirm the relationship in Question 1?** Here, you should specify the variables to be plotted on the x-axis and y-axis to graphically confirm the relationship identified in Question 1. 3. **What is the theoretical slope of the line on the graph in Question 2?** In this part, you are asked to identify the theoretical slope of the line obtained from the graph described in Question 2. 4. **What are the units of $ k $ (in mks units)?** For this question, determine the units of the constant $ k $ in the standard metric system units (meters, kilograms, seconds).**Note:** These questions are part of an educational problem set designed to help students understand and analyze the relationship between force and distance in a physical context.

To determine Relation between force and distance in spring

1. What is the relationship you are testing between force and distance? 2. A graph of what vs. what would be required to confirm the relationship in Question 1? 3. What is the theoretical slope of the line on the graph in Question 2? 4. What are the units of k (in mks units)?

1. What is the relationship you are testing between force and distance? 2. A graph of what vs. what would be required to confirm the relationship in Question 1? 3. What is the theoretical slope of the line on the graph in Question 2? 4. What are the units of k (in mks units)?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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