1. ME 101: Measurement Demonstration (MD3)
Vectors, Statics and Dynamics Measurements
Mechanical Engineering 101
University of Kentucky

2. Reminders / Homework Homework #3 – Due Wednesday 10/6 - Today
Wickert - 3.2, 3.4, 3.5, 3.13
Computer Demonstration 2 (CD2) – Due Friday 10/8
Career Fair – Wednesday 10/13
Student Center Grand Ballroom
12:00 PM – 4:00 PM
5 Extra Credit Points
3 Business Cards (Stapled to a sheet of paper)
Mechanical Engineering 101
University of Kentucky

3. Introduction Purpose: To examine spring-mass systems
Determine spring forces
Determine deformations
Determine spring constants
Drawing FBD’s
Simple harmonic motion
Mechanical Engineering 101
University of Kentucky

4. Experiment Experiment Materials Experiment Tools Two springs
One large
One small
Different spring constants
Weight Basket
Weights/Masses
Experiment Tools
Linear Scale (Use cm Scale)
Scale (Grams)
Protractor (Degrees)
Stopwatch (Seconds)
Mechanical Engineering 101
University of Kentucky

5. W Problem A mass hangs from a spring Causes stretch in the spring
Displaced a distance d from its unstretched length
How do we describe this system?
Unstretched Length
Equilibrium
Stretch (d)
Equilibrium
Position W
Mechanical Engineering 101
University of Kentucky

6. Hooke’s Law Springs are governed by Hooke’s law: where:
F is the force (or weight) applied to the spring
x is the distance displaced
k is the spring constant
Determine spring constant of spring at front of room.
Mechanical Engineering 101
University of Kentucky

7. x W Static Behavior A mass of known weight hangs from a spring
Allow system to come to rest
What is the spring constant k?
How do you solve problem?
Step 1: Draw a Free Body Diagram
Step 2: Set the force equal to the weight of the mass
Step 3: Measure the displacement
Step 4: Solve for k W x
Mechanical Engineering 101
University of Kentucky

8. x W Static Behavior Step 1: Draw a Free Body Diagram
Step 2: Set the force equal to the weight of the mass
Step 3: Measure the displacement
Step 4: Solve for k
Step 1: Draw a Free Body Diagram
Step 2: Set the force equal to the weight of the mass
Step 3: Measure the displacement
Step 4: Solve for k W x
Mechanical Engineering 101
University of Kentucky

9. Static Behavior: 2 Springs
What is the deflection with two springs? k1 k2
Mechanical Engineering 101
University of Kentucky

10. Static Behavior: 2 Springs
What are the forces in the springs? W k1 k2
F = (k1 + k2) ∆x
Mechanical Engineering 101
University of Kentucky

11. Static Behavior: 2 Springs
Step 1: Draw a Free Body Diagram
Step 2: Set the force equal to the weight of the mass
Step 3: Measure the displacement
Step 4: Solve for k W F1 F2
Step 1: Draw a Free Body Diagram
Step 2: Set the force equal to the weight of the mass
Step 3: Measure the displacement
Step 4: Solve for k
F = (k1 + k2) ∆x
Mechanical Engineering 101
University of Kentucky

12. Dynamic Behavior A block hangs from a spring
Pull down 10 cm and release
Bounces up and down at a rate of X times every second
How could this rate be increased?
Mechanical Engineering 101
University of Kentucky

13. Dynamic Behavior Which is correct? You may choose any of:
increase the mass
decrease the mass
push it faster
make the spring stiffer
make the spring less stiff
pull it down farther
don’t pull it down as far
other?
Which is correct?
Mechanical Engineering 101
University of Kentucky

14. Spring Constant & Period
The period T (or frequency f) of an oscillator is related only to:
the stiffness (k) of the restoring force
the inertia (m) of the system
It does not tell you anything about how the system got started
The frequency is independent of the amplitude
The period (or frequency) of an oscillator is related only to the stiffness (k) of the restoring force and the inertia (m) of the system. It does not tell you anything about how the system got started and is independent of the amplitude.
Mechanical Engineering 101
University of Kentucky

15. Spring Constant & Period
The period (or frequency) of an oscillator is related only to the stiffness (k) of the restoring force and the inertia (m) of the system. It does not tell you anything about how the system got started and is independent of the amplitude.
Mechanical Engineering 101
University of Kentucky

16.  2 m  4 k Problem Therefore, m = 8.0 kg
A 2.0 kg block hangs from a spring and oscillates with a period T = 1 s
What mass of block, hung from the same spring, would have T = 2 s?
 2 m
 4 k
Therefore, m = 8.0 kg
Mechanical Engineering 101
University of Kentucky

17. Key Concepts
The spring constant can be found from Hooke’s law or the period
Static equilibrium means the sum of the forces = 0
Dynamic motion results when sum of the forces ≠ 0
The period T depends on k and m only
Mechanical Engineering 101
University of Kentucky

18. Resonance Tacoma Narrows Bridge We’ll see this in later labs!
Mechanical Engineering 101
University of Kentucky

19. Lab Procedure – Part I – Spring Calibration
Select one of the springs provided to you. Make sure you indicate which spring it is so you can keep track of it during the experiment.
Hang the spring vertically and measure the location of the tip. This is your starting point for that spring.
Weigh the basket and hang from the spring. Add weights to the basket until it deflects. Wait for the system to come to rest. Measure the deflection from the zero point and record it as your offset. Record the deflection in cm (x) and weight (F) in Newtons. This is the first point on your curve.
Increment the weight attached to the spring by adding a small mass. Make sure the system comes to rest. Measure and record the deflection and total applied force. Repeat 4 times.
Plot all 5 points in Excel. Using the curve fitting function, calculate the slope of the curve to determine the spring constant k.
Repeat for the other spring. Make sure to include your table and plots for each spring (1 page for each spring).
Mechanical Engineering 101
University of Kentucky

20. Lab Procedure – Part II – Static Measurements
Attach one end of each of the springs to the table, 30 cm (12 inches) apart.
Attach the mass hanger to the end of the two springs. Add weights to the basket until both springs begin to deflect. Wait for the system to come to rest. This will be your zero point. Draw the FBD of the system.
Measure the angle of the springs with respect to the horizontal plane and the displacement of the springs.
Find the magnitude F and direction for each of the vectors. Write them in equation form (F = Fxi+Fyj).
Determine the net force in each direction (Fx and Fy). Are they equal to zero? Should they be?
 Repeat steps 3-5 for 4 other loads on the system.
Mechanical Engineering 101
University of Kentucky

21. Lab Procedure – Part III – Dynamic Measurements
Using the larger of the two springs, hang it vertically and attach a mass of approximately 140 grams (14 N) to the spring.
Pull the spring down a measurable distance and allow it to oscillate.
Using the stopwatch, record the number of times the system oscillates in 30 seconds.
Calculate the period and frequency of the spring-mass system.
Using the equation for frequency and the known parameters of the system, calculate the spring constant. Compare this value with that measured in Part I.
Mechanical Engineering 101
University of Kentucky

22. Reminders / Homework Homework #4 – Due Wednesday 10/13
Wickert , 3.17, 3.29, 3.30
Computer Demonstration (CD2) – Due Friday 10/8
Career Fair – Wednesday 10/13
Student Center Grand Ballroom
12:00 PM – 4:00 PM
5 Extra Credit Points
3 Business Cards (Stapled to a sheet of paper)
Measurement Demonstration (MD3) – Friday 10/8
Attendance is mandatory, no make-ups will be given
Get to class early if possible, we will start on time it takes the full 50 minutes
Same team assignments as MD2 (Posted on BlackBoard)
Mechanical Engineering 101
University of Kentucky