me 101: measurement demonstration (md3) vectors, statics and dynamics measurements mechanical...

ME 101:Measurement Demonstration (MD3)

Vectors, Statics and Dynamics Measurements

Mechanical Engineering 101University of Kentucky

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 – http://www.uky.edu/CareerCenter/

– 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 101University of Kentucky

Introduction

Purpose:

To examine spring-mass systems– Determine spring forces

– Determine deformations

– Determine spring constants

– Drawing FBD’s

– Simple harmonic motion

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Experiment

Experiment Materials• 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)

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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?

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Unstretched Length

Equilibrium

Stretch (d)

EquilibriumPosition

W

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

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xkF

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?

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xW

xkF

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

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xWxkF

Static Behavior: 2 Springs

What is the deflection with two springs?

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k1

k2

1 2

1 1F x

k k

Static Behavior: 2 Springs

What are the forces in the springs?

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W

k1 k2

F = (k1 + k2) ∆x

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

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W

F1F2

F = (k1 + k2) ∆x

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?

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Dynamic Behavior

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?

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Which is correct?

• 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

Spring Constant & Period

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Spring Constant & Period

Mechanical Engineering 101University of Kentucky

mkTf

2

1/1

kmT 2

mkfn 2

Problem

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?

Mechanical Engineering 101University of Kentucky

2T mk

2 4

Therefore, m = 8.0 kg

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

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Resonance

• Tacoma Narrows Bridge

• We’ll see this in later labs!

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Lab Procedure – Part I – Spring Calibration

1. 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.

2. Hang the spring vertically and measure the location of the tip. This is your starting point for that spring.

3. 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.

4. 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.

5. Plot all 5 points in Excel. Using the curve fitting function, calculate the slope of the curve to determine the spring constant k.

6. Repeat for the other spring. Make sure to include your table and plots for each spring (1 page for each spring).

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Lab Procedure – Part II – Static Measurements

1. Attach one end of each of the springs to the table, 30 cm (12 inches)

apart.

2. 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.

3. Measure the angle of the springs with respect to the horizontal plane and

the displacement of the springs.

4. Find the magnitude F and direction for each of the vectors. Write

them in equation form (F = Fxi+Fyj).

5. Determine the net force in each direction (Fx and Fy). Are they

equal to zero? Should they be?

6.  Repeat steps 3-5 for 4 other loads on the system.

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Lab Procedure – Part III – Dynamic Measurements

1. Using the larger of the two springs, hang it vertically and attach a mass

of approximately 140 grams (14 N) to the spring.

2. Pull the spring down a measurable distance and allow it to oscillate.

3. Using the stopwatch, record the number of times the system oscillates

in 30 seconds.

4. Calculate the period and frequency of the spring-mass system.

5. 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.

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Reminders / Homework

• Homework #4 – Due Wednesday 10/13– Wickert - 3.15, 3.17, 3.29, 3.30

• Computer Demonstration (CD2) – Due Friday 10/8

• Career Fair – Wednesday 10/13 – http://www.uky.edu/CareerCenter/

– 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 101University of Kentucky