Slinky Secrets Revealed Math Lab 23. Purpose of Lab Demonstrate that the force used to stretch a spring is proportional to the amount it stretches. Find.

Slides:

Advertisements

Similar presentations

Lab Equipment Overview

Advertisements

Next Level Chromatography.

Spring Force. Compression and Extension  It takes force to press a spring together.  More compression requires stronger force.  It takes force to extend.

Section 3.6 Variation. Direct Variation If a situation gives rise to a linear function f(x) = kx, or y = kx, where k is a positive constant, we say.

3.4 – Slope & Direct Variation. Direct Variation:

Variation Variation describes the relationship between two or more variables. Two variables, x and y, can vary directly or inversely. Three or more variables.

Table of Contents Direct and Inverse Variation Direct Variation When y = k x for a nonzero constant k, we say that: 1. y varies directly as x, or 2. y.

Direct Variation: y varies directly as x (y is directly proportional to x), if there is a nonzero constant k such th at 3.7 – Variation The number k is.

Springs. Hooke’s Law Any spring has a natural length at which it exerts no net force on the mass m. This length, or position, is called the equilibrium.

REMEMBER: A number can be negative or positive as shown in the number line below: Negative Numbers (-) Positive Numbers (+)

Identify, write, and graph an equation of direct variation.

PHYSICS InClass by SSL Technologies with S. Lancione Exercise-42

Laboratory Equipment, Safety and Procedures

Inverse Variation Inverse Variation. Do you remember? Direct Variation Use y = kx. Means “y v vv varies directly with x.” k is called the c cc constant.

Algebra II Writing Equations of Lines. Algebra II Equations of Lines There are three main equations of lines that we use:  Slope-Intercept – if you know.

Direct Variation What is it and how do I know when I see it?

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Direct Variation 5-4. Vocabulary Direct variation- a linear relationship between two variable that can be written in the form y = kx or k =, where k 

Direct Variation What is it and how do I know when I see it?

Elastic potential energy

Language Goal  Students will be able to verbally express direct variation. Math Goal  Students will be able to identify, write, and graph direct variation.

3.6 – Proportional & Nonproportional Relationships

20S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Real Number System Lesson: LMP-L5 Direct Variation Direct Variation Learning Outcome B-4 LMP-L5.

5-4 Direct Variation Warm Up 1. Regina walked 9 miles in 3 hours. How many miles did she walk per hour? 2. To make 3 bowls of trail mix, Sandra needs 15.

ME 101: Measurement Demonstration (MD3)

Springs Web Link: Introduction to SpringsIntroduction to Springs the force required to stretch it  the change in its length F = k x k=the spring constant.

Chapter 14 VIBRATIONS AND WAVES In this chapter you will:  Examine vibrational motion and learn how it relates to waves.  Determine how waves transfer.

Lines and Slopes Table of Contents Introduction Drawing a Line - Graphing Points First Slope - Calculating Slope - Finding Those Slopes.

  Volume is defined as the amount of space taken up by a three-dimensional object. What is Volume.

Introduction to Linearization ( No units, no uncertainties, just the core idea ) The purpose of linearization is to get the equation that describes real.

Slopes and Direct Variation December 9, Review Slope Slope – Rise Run (-1, -4) and (2, 2)

Chapter 2 More on Functions Copyright ©2013, 2009, 2006, 2005 Pearson Education, Inc.

Direct Variation What is it and how do I know when I see it?

Direct Variation Section 1.9.

1.11 Modeling Variation.

Lesson 6-9: Variation Objective: Students will: oFind the constant of variation and setup direct and inverse variation equations oUse variation equations.

5-4 Direct Variation Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

k is called the constant of variation or constant of proportionality.

Springs and Hooke’s Law Physics 11. Springs A mass-spring system is given below. As mass is added to the end of the spring, what happens to the spring?

Starter 1.What is the spring constant for this spring? 2.What is the meaning of the y-intercept? 1.What is the spring constant for this spring? 2.What.

Lesson 3 Relationships. Stretching a spring What is the input variable here and what is the outcome variable?

Adding two numbers together which have the same absolute value but are opposite in sign results in a value of zero. This same principle can be applied.

Direct Variation y = kx. A direct variation is… A linear function Equation can be written in the form; y = mx ; m  0 ory = kx ; k  0 The y-intercept.

Writing a direct variation equation. write a direct variation problem when y = 20 and x = 10 y = kx 20 = k·10 k = 2 y = 2x.

Direct Variation 88 Warm Up Use the point-slope form of each equation to identify a point the line passes through and the slope of the line. 1. y – 3 =

Definition of SHM Objectives Define simple harmonic motion. Select and apply the defining equation for simple harmonic motion. Use solutions to.

PHYSICS InClass by SSL Technologies with Mr. Goddard Hooke's Law

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Do - Now (-2, 1) & (4, 7) (1, 0) & (0, 4) (-3, -4) & (1, 6)

2.2 Direct Variation P68-70.

Math CC7/8 – April 24 Math Notebook: Things Needed Today (TNT):

Warm Up Solve each proportion. = = 1. b = y = 8 = = m = 52

Springs Forces and Potential Energy

Elastic Forces Hooke’s Law.

Direct Variation Chapter 8 Section 8.9.

Elastic Objects.

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

2.5 Model Direct Variation

Lesson 5-2 Direct Variation

Virtual Lab: Exploring Newton’s 2nd Law

Prediction and Accuracy

Objective Identify, write, and graph direct variation.

Linear Relationships Graphs that have straight lines

5.3 – direct variation Textbook pg. 301 Objective:

Energy Part 3 – Hooke’s Law.

Linear proportional relationship Linear non-proportional relationship

A spring is an example of an elastic object - when stretched; it exerts a restoring force which tends to bring it back to its original length or equilibrium.

Lab Extension Post-Lab

Presentation transcript:

Slinky Secrets Revealed Math Lab 23

Purpose of Lab Demonstrate that the force used to stretch a spring is proportional to the amount it stretches. Find the constant of proportionality.

Math Principles Direct variation, scatter-plot, slope, measuring with a ruler, linear regression.

What It’s All About The amount of force (F) needed to stretch a spring varies directly as the amount of stretch (x). The equation that describes this is: F =(const)x.

What It’s All About In this lab the stretching force is provided by the weight of nuts hung on the end of a spring (slinky). Since this weight is proportional to the number of nuts, the equation will be modified to the following where N is the number of nuts: N = kx

What It’s All About Marks will be made on the background (chalk board or white board) as several nuts are successively placed on the hanger. Distances between the marks are measured for later analysis in which the constant of proportionality will be determined.

Slinky Secrets Revealed Mark the starting point: With the spring hung with no added weights, stabilize it and mark the bottom of the spring. All measurements will be referenced from this point. Make sure the student marking this and following positions has his eyes level with the bottom of the spring so as to accurately mark the true position.

Slinky Secrets Revealed Gently hang one nut on the hanger, stabilize the spring, mark the position, and label with “1”. Again, make sure eye level is at the bottom of the spring so as to place an accurate mark.

Slinky Secrets Revealed One at a time, add nuts (up to a total of four) to the hanger. Each time mark the position of the bottom of the spring and record the number of nuts beside each mark. The picture below shows the marks and labeling after all four nuts have been attached.

Slinky Secrets Revealed Measure the distances: Using a centimeter ruler, measure the distances of each position of the spring (1, 2, 3, & 4) from the zero mark as shown to the left.

Slinky Secrets Revealed Putting it all together: Make a scatter-plot of the points with a large black marker.

Slinky Secrets Revealed Finding the constant of proportionality: Determine the constant of proportionality (k, also the slope of the line) for this line as follows:

Slinky Secrets Revealed Finding the constant of proportionality: Determine the constant of proportionality (k, also the slope of the line) for this line as follows: Since the line goes through the origin, use (0, 0) as one point and (36.4, 4) as the other. The slope (and therefore k) is:

Slinky Secrets Revealed Finding the constant of proportionality: Determine the constant of proportionality (k, also the slope of the line) for this line as follows: Since the line goes through the origin, use (0, 0) as one point and (36.4, 4) as the other. The slope (and therefore k) is:

Slinky Secrets Revealed Finding the constant of proportionality: Determine the constant of proportionality (k, also the slope of the line) for this line as follows: Since the line goes through the origin, use (0, 0) as one point and (36.4, 4) as the other. The slope (and therefore k) is:

Slinky Secrets Revealed Finally, the complete linear function is: F =.10989x