EGH166 Hands-on Lab

## Lab 2: Springs and Levers

#### Introduction

##### Background

Potential energy is a resource that is often overlooked. Powering devices with electro-mechanical devices is often the first thought, but not always the most efficient.  Springs, gravity, and other forms of stored energy, used with leverage, can provide a simple and effective means for actuating devices. For example, cranking the handle of a music box compresses a spring, which drives the device.

##### Purpose

The purpose of this lab is to familiarize you with the properties of some basic types of springs, and to use the concept of leverage in building a scale.

##### Basic Principles

In this lab write-up, we will cover some basic principles behind:

1)            Properties of three types of springs, and

2)            Leverage.

##### Lab Experience

The lab experience will encompass:

1)            Standard measurements of spring constants,

2)            Independent measurements of spring constants, and

3)            Building a scale.

#### Properties of Springs

##### Introduction

A spring is any material that is designed to resist a change in shape. In contrast, a solid object tries to keep its form. The degree to which a material resists a change in form is called the spring constant.  The spring constant defines the amount of force that must be generated in order to stretch, compress, bend or deflect a spring by a certain amount.

There are several types of springs; each is best suited to oppose a change in shape in a particular direction.  Compression springs are the most commonly used type.

##### Compression Springs

Compression springs are found in a wide range of sizes and strengths. From tiny, light duty springs found in a lock barrel, to large, heavy-duty shock absorber springs in an automobile. The spring constant of compression springs defines the amount of the decrease in the length that the spring undergoes under a certain load.

##### Spring Constant of compression springs

The spring constant (K) demonstrates a linear relationship between Force and Displacement.  The linear nature of springs is acceptable for most springs over their typical range. However, the actual relationship between Force and Displacement is more complicated.  For practical purposes, assuming a linear relationship is a standard practice.

When assuming a linear relationship, it is reasonable to treat any known position of a spring as its zero position and use ‘F = K x’ from that reference point.

##### Interplay of Force and Distance

Consider a 2400-pound automobile with 4 identical shock absorbers.  If the car is equally balanced over each tire, then each shock absorber will support 600 lbs. (ignoring angles and lever arms in the suspension system).  If the shock absorbers have a spring constant of 100 lbs/inch, how much are the springs compressed from their no-load position?

F=Kx               F = Force on each spring (600 lbs)

K = spring constant (100 lbs/inch)

x = Compression of spring (inches)

x = 600 lbs / (100 lbs/inch) = 6 inches

Following the same problem, if a 200-lb. man sat in the car, equally distributed over all 4 tires, how much lower would the car sit?

It is NOT necessary to add the 200 lbs. to the 2400lb weight of the car and redo the problem.  One can simply treat this as a new problem, calling the current position of the car zero.

F = K x            F = 200/4 = 50 lbs. on each tire

K = 100 lbs./inch

x = 50 lbs. / (100 lbs./inch) = 1/2 inch

The car sunk an additional 0.5” when the man sat in the car.  If the weight of the car and the man were taken into account and the problem was referenced from the no-load position of the shock absorbers then the answer would be identical, but changing the reference position of the car simplified the problem.

##### Tension Springs

Tension springs are another style of spring that resists change in stretching.  The formula is identical (F = K x) for relating forces to change in length. However, x = the increase in length for tension springs.

##### Springs

Torsion springs are designed to resist twisting. Torque is rotational force, and degrees or radians are rotational distance.  Instead of using the formula F = K x for linear displacement, we use t = K q.  Where t is the torque and q is the angular displacement.  Torque is measured as a Force x Distance (moment arm).  Consider a wrench, if a mechanic is tightening a bolt and he/she holds their hand 6 inches away from the axis of the bolt and pulls with 20 lbs. of force this produces 1/2 x 20 = 10 ft lbs. of torque on the bolt.

Torsional springs are used to move or support rotating objects such as hinges or levers.  A mousetrap uses a cocked torsion spring as its stored energy.  A tape measure is a torsion spring, when the tape is pulled out of its case the coil inside becomes very tight, the tape is pulled back in to increase the size of the coil (trying to achieve a no-load position).

##### Springs

Leaf springs are yet another type of springs They are used to provide rigid support (high spring constant) where there is limited space along the axis of support.  Leaf springs are often used as a rear shock absorber in trucks.

##### Of Springs

A simple version of a spring is a thin piece of metal that flexes, typically a piece of spring steel (a type of steel with good elastic properties).

This hinge will attempt to open because the spring force of the flexed metal. The spring steel is mounted on one end and free to slide on the other.

Some other forms of "springs" are rubber bands, bunjy cords and other elastic cords. Any object that flexes under load has some spring properties.  For structures and beams the formulas for computing the deflection can be more complicated, but the behavior is the same: the object produces a restoring force attempting to return to its no-load position.

#### LEVERAGE

##### Introduction

Leverage is the basis for the simplest 'machines' such as wheelbarrows, pry bars and car jacks. A lever is simply a method of transferring work from one location to another.

##### Work and Force Relation

Work is calculated as Force x Distance:

W (Ft-lbs) = F (lbs) x D (feet)

Incidentally Work and Torque have the same units; the D in each of the formulas refers to a different distance.  For torque, the D is the moment arm, or distance away from a rotating axis (a distance perpendicular to the line of force). For work, the distance is calculated in the direction of the force.  If a 10-lb. object is lifted 5 inches then 50 in-lbs. of work have been accomplished, but no torque is present.

##### Example ofLeverage

For example, if a pry bar is used to lift the base of a heavy object:

The lifting force is greater than the force applied to the pry bar because the operator has a mechanical advantage: He/she is farther away from the fulcrum than the load. If the operator supplies 100 lbs. of force, it would generate 800 in-lbs. about the fulcrum, which translates into 800/2 = 400 lbs. of force to lift the object. However, if no motion of the object occurs, then no work is done.

Work is done when the object is moved and the operator supplies the force of 100 lbs. over a certain distance.  If the object was lifted 1 inch then the work done on the object is:

W = F x D       F = Force applied to object = 400 lbs.

D = Distance the object is moved = 1 inch

W = 400 x 1 = 400 in-lbs.

If 400 in-lbs. of work were done on the object then the operator must have done 400 in-lbs. of work.

W (operator) = 400 in-lbs. = F x D

F (operator) = 100 lbs

D (operator) = 400 in-lbs. / 100 lbs = 4 inches

Notice the trade off between force and distance. The operator uses a low force to lift the object but he/she must move a greater distance to accomplish the work.  This principal applies throughout all forms of mechanical advantage: "you can't get something for nothing,” force gained means displacement wasted.

#### LAB EXPERIENCE

Make sketches of equipment used in class; include them in your lab write-up.

##### Standard Measurements

Determine the spring constant of all compression, tension and torsional springs provided.  Be sure to take adequate data in order to get accurate results.

##### Independent measurements

Compute the spring constants of two tension springs hanging in a V formation.  DO NOT separate them and compute them separately.  Hint: the sum of forces acting on an object at rest or moving at a constant speed is zero.

(Some guy called Newton said that once.)  Be sure to record your set up so that it could be duplicated.

##### Questions

1)            Produce a graph for each of the three types of springs tested (at least 3 graphs total).  Are the springs perfectly linear?  If your graphs are curved slightly is this due to the springs or the experimental method?  Plot at least three data point per graph.

2)            What are the two values of K for the "V" hanging springs?  Explain (with calculations) the method used to find the values.

##### Build a Scale

Using the items provided and some creativity, build a scale capable of weighing up to 250 lbs.  Calibrate it and demonstrate its effectiveness.  Think about safety issues, and check your apparatus with your lab instructor before testing it.

##### Questions

3)            How accurate is your scale?  Calculate this using ± values for each of your parameters.  Is this accuracy acceptable for a simple scale?  Explain.

4)            Comment on the safety of the scale.  Describe any possible hazards either from failure of the device, or through use or miss-use of the scale.

#### LAB REPORT

##### Format

q       Lab reports must be done individually

q       Follow given lab report format.

q       Maximum 4-5 pages (including figures and tables)

##### General Guidelines

q       Cover page

q       Description of Experimental Apparatus

q       Introduction/Background

q       Description of tests. Obtain graphs and sketch test setups. Graphics: Tension, Compression, and Torsion.

For Each Spring Type

q       Plot weight vs. Distance.

q       Provide sketch of test setup

q       Derive equations. Compute spring constants.

Plot weight vs. Distance.

Provide sketch of test setup

Derive equations. Compute spring constants.

q       Description of "V" test. Computation of spring constants.

q       Description of scale design. Development of scale. Include equations and sketches. Comment on accuracy.

q       Analysis of results/Summary.