MECE 102: Engineering Mechanics Lab
A First Year Course in
Newtonian Mechanics, Experimentation,
and Computer Tools
Created by the Faculty of the Mechanical Engineering
Department in the Kate Gleason College of Engineering at RIT
Week 8 Lecture
Hooke’s Law
This week we will study the response of
Linear Elastic Materials.
• A spring with a hanging mass will be used in Lab to
demonstrate the response of a Linear Elastic material.
iCLICKER:
The week 8 Lab Experiment studies Hooke’s Law for
linear elastic materials. Which one of the following
materials would NOT be considered a linear elastic
material?
• Select your Answer:
A.
B.
C.
D.
E.
Steel
Aluminum
Rubber
Titanium
None of the above.
iCLICKER:
The week 8 Lab Experiment studies Hooke’s Law for
linear elastic materials. Which one of the following
materials would NOT be considered a linear elastic
material?
• Select your Answer:
A.
B.
C.
D.
E.
Steel
Aluminum
Rubber
Titanium
None of the above.
iCLICKER:
Which phase of matter is Hooke’s Law valid for?
• Select your Answer:
A.
B.
C.
D.
Gas
Liquid
Solid
Gas and Solid
iCLICKER:
Which phase of matter is Hooke’s Law valid for?
• Select your Answer:
A.
B.
C.
D.
Gas
Liquid
Solid
Gas and Solid
FORMULATE: State the Known Information
• Given the mass, m, of a dead weight suspended from a
linear elastic spring
• Determine the spring constant, K, of the spring, and the
change in energy stored within the spring as a result of the
work done by mass, m, upon the spring as the spring, S,
moves from its initial position, i , to its final position, f.
FORMULATE: Identify the Desired Information
iCLICKER:
For our Week 8 experiment, which one of the
following assumptions is TRUE?
• Select your Answer:
A. The initial velocity of the mass hanging on the spring is not
zero.
B. The mass of the spring being analyzed is negligible.
C. Heat Transfer is significant between the spring and its
surroundings.
D. Elastic Spring Energy is negligible.
iCLICKER:
For our Week 8 experiment, which one of the
following assumptions is TRUE??
• Select your Answer:
A. The initial velocity of the mass hanging on the spring is not
zero.
B. The mass of the spring being analyzed is negligible.
C. Heat Transfer is significant between the spring and its
surroundings.
D. Elastic Spring Energy is negligible.
FORMULATE: Identify Assumptions
FORMULATE: Identify Assumptions
FORMULATE: Identify Assumptions
What other Engineering relationship is commonly associated with
Hooke’s Law?
FORMULATE: Identify Assumptions
What other Engineering relationship is commonly associated with
Hooke’s Law?
𝑆𝑡𝑟𝑒𝑠𝑠 = 𝐸 𝑆𝑡𝑟𝑎𝑖𝑛
𝜎=𝐸𝜀
This relationship will be studied extensively in your
Strength of Materials and Materials Science Courses.
CHART: Schematic Diagram
Note that the Neutral
Condition of the spring, with
no external mass applied, is an
important position to consider
when analyzing the system.
Figure 8.1: Schematic Diagram of a mass suspended from a
spring in tension.
CHART: Schematic Diagram
Figure 8.1: Schematic Diagram of a mass suspended from a
spring in tension (zoomed-in).
CHART: Schematic Diagram
Figure 8.3: Schematic Diagram of a spring unloaded, loaded in
tension, and loaded in compression.
CHART: Free Body Diagram
CHART: Data Table
• Each row in the STATE TABLE corresponds to one unique position of
the Spring.
• This Lab Experiment will reinforce the importance of defining an
appropriate elevation datum, z = 0, and displacement datum, d = 0.
Hooke’s Law
• Hooke’s Law states that Strain is directly related to Stress.
• For this experiment we are investigating the response of a solid linear
elastic material under either compression or tension.
• In the case of a Spring, Hooke’s Law states that the restoring force
exerted by the material is proportional to the magnitude of
displacement, and the direction of the restoring force is in the opposite
direction of the displacement.
EXECUTE: Apply and Simplify the Governing Equations
Applying Newton’s Laws when analyzing the FBD of the Spring-Mass
system gives:
Recall that the work done by the Mass upon the Spring from state i to
state f is the integral of the fore along the displacement:
EXECUTE: Apply and Simplify the Governing Equations
Based on Hooke’s Law:
When the spring achieves it final equilibrium state after the Mass is
added, the spring deflected length will be z1:
EXECUTE: Apply and Simplify the Governing Equations
Recall that the work done on the Spring by the Mass from state i to state
f is given by:
EXECUTE: Apply and Simplify the Governing Equations
Similarly, the work done by the Spring on the Mass from state i to state f
is given by:
EXECUTE: Apply and Simplify the Governing Equations
EXECUTE: Apply and Simplify the Governing Equations
The important equations used in the Week 8 Lab Experiment are
summarized below:
Example Problem
A 200 gram mass is suspended from a spring
causing it to stretch from 5 cm to 7 cm.
What is the spring constant [N/m] of the spring?
Example Problem
A 200 gram mass is suspended from a spring
causing it to stretch from 5 cm to 7 cm.
What is the spring constant [N/m] of the spring?
K = 98.1 N/m
BONUS POINT Problem
A spring has an unloaded length of 37 cm and a
spring constant of 1500 N/m.
What is the new length [cm] of the spring if a
75 N compressive load is applied to the spring?
Example Problem
A spring has an unloaded length of 37 cm and a
spring constant of 1500 N/m.
What is the new length [cm] of the spring if a
75 N compressive load is applied to the spring?
The new length of the spring is 32 cm.
Week 8 Lab Experiment
Homework
• Prior to LAB tomorrow
• Read section 8.2 of the textbook
• Watch LAB Videos
• Complete the on-line LAB quiz in myCourses
• Attempt to solve all assigned Homework problems in your
logbook before RECITATION.
• WEEK 8 Problem Set:
• From Section 8.5: Problems 2, 3, 5, 6, 7
• Lab Report is due Monday by 6pm!
• The Scribe must upload the LAB REPORT to the myCourses Dropbox.
Questions??
Example Problem
A spring has an unloaded length of 37 cm and a
spring constant of 1500 N/m.
What is the new length [cm] of the spring if a
300 N compressive load is applied to the spring?
The new length of the spring is 17 cm.