ENGR 103 Lab #3 Graphical Integration

First Law of Thermodynamics • Energy can be converted from one form to another, but total energy remains

constant (energy cannot be created or destroyed).

From Lab #2: Forms of Energy • Potential Energy

• Spring PE = ½ kx2

• Gravitational PE = mgz

• Kinetic Energy • KE = ½ mv2

• How does a toy dart gun work?

Dart Gun • Stored Energy in Spring by applying a force through a displacement (work)

• Converted potential energy in spring to kinetic energy in dart and moving components of gun

• Converted KE dart into PE dart

• Where did the rest of the energy go?

• Where did we get the magic formula “Spring PE = ½ kx2” ?

Work • For a constant force applied over a displacement • Work = Force • displacement • Notice it is the area under the curve

Work on a Spring (Stored PE) • Work = force x displacement, but

• Force in spring is a function of displacement • Constant slope = k (linear spring)

• Hooke’s Law: k = F/x (slope of the function)

• Work compressing spring = area under the curve

• Therefore Work (Area of Triangle)

PE = ½ F x

Substituting Hooke’s Law in for F: PE = ½(x*k)x

PE = ½ kx2

Work on a non-linear spring? • Area under the curve • Don’t have a formula? • No problem Graphical Integration

A non-linear spring in action

Lab # 3 Given Data:

Deflection[ft] Force [lbf]

0 0

0.1 0.015

0.2 0.12

0.3 0.405

0.4 0.96

0.5 1.875

0.6 3.24

0.7 5.145

0.8 7.68

0.9 10.935

1 15

1.1 19.965 0






0 0.2 0.4 0.6 0.8 1 1.2

Fo rc


Rod Deflection

Graphite Fishing Rod Stiffness

• The fishing rod is a non-linear spring (k is not constant)

• The PE stored in the fishing rod can be found by integrating the Force vs Deflection curve below

• The bait being cast by the rod weights 0.06 lbf and has a velocity just before the fishing rod “snaps” of 44 ft/s

• When the fishing rod “snaps” all of the PE of the fishing rod is transferred to KE of the bait

Lab 3 – Graphical Integration – Due Mon, Sept 17th

All work should be done in the gravitational system of units (ie: ft, lbf, ft∙lbf)

1. Calculate the spring energy stored in the rod just prior to release of the bait as a function of the bend in the rod. An expert caster will create maximum deflection in the rod.

2. Calculate the speed of the bait as it leaves the rod assuming all the fishing rod’s stored energy is transferred to the bait as Kinetic Energy. Assume the velocity imparted by the cast motion before the rod “snaps” is 44 ft/s, so the total energy of the bait is KE @ 44 ft/s + spring energy stored in rod.

3. Using a projectile calculator calculate the cast distance of the fishing rod.
Lab # 3 Documentation • Problem Statement (10 points, plus 5 points for neatness)

• Include all known information • State what is being solved

• Assumptions (10 points) • A minimum of 2 • Don’t include facts, equations…

• Governing Equations (10 points) • Energy / work and force equations • Area equations • Unit conversion equations (keep all units in USC units)

• Calculations (50 points) • Easy to follow • Show examples (2-3) of all calculations done multiple times and then tabularize your results • Include units with all values (USC) • Results should be highlighted and report to 3 sig figs

• Summary and Conclusions (15 points) • Results • 2-3 comments / observations about the lab

Notes • To calculate the velocity of bait as it leaves the rod:

a) calculated the KE due to the velocity of the cast of 44 ft/s,

b) find the total KE by adding the KE due to cast to the PE of the rod when deflected. You are assuming that all the PE stored in the rod will transfer to KE of the bait.

c) using this total KE, solve for the velocity of the bait.

• If you choose to do the calculations in excel, make sure to print out your spreadsheet to turn in with your lab report. You must still document everything including your calculation procedure on Engineering Paper.

• Lab #3 should be done either individually or in groups of two. If you choose to do groups of two, the students must be from the same section.

• When you use the projectile calculator – pay attention to units!

• Pay attention to units in your calculations and use gc when appropriate.

ENGR 103
First Law of Thermodynamics
From Lab #2: Forms of Energy
Dart Gun
Work on a Spring (Stored PE)
Work on a non-linear spring?
A non-linear spring in action
Lab # 3 Given Data:
Lab 3 – Graphical Integration – Due Mon, Sept 17th
Lab # 3 Documentation

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