### Introduction: (Initial Observation)

This project consists of two main parts. In the first part we study electric motors principles and how they work. In this part we may also build a working model of an electric motor. In the second part we learn about efficiency of electric motors and how it is defined and calculated. we then study the factors that may affect the efficiency of electric motors.

**Note:** When we talk about factors affecting the efficiency of an electric motor, we could be talking about design factors or use factors.

Design factors are things like the type, diameter and number of loops of wires used to make the electric motor. Another design factor can be the distance between internal components of the motor (such as the distance between rotor and stator).

Use factors are things like voltage and load that can be set by the user. For example a small electric motor may work by supplying any voltage from 1 to 12 volts, but it may be more efficient when used with 6 volts. Also the same motor may be most efficient when used with loads about 50 g-cm. If you don’t know what is g-cm or grams-centimeters don’t worry, I will explain it later in this page.

Here in this project we will only discuss the efficiency based on load. That is what most users of electric motor need to know. If you want to change the focus of your project from use factors to design factors, contact your project advisor for support.

### Information Gathering:

**Step 1:** To start Click Here to see the principles of electric motor. Try to perform the experiments suggested in this section. If you like to make an electric motor as a part of this project, Click here to see how you can make an electric motor. Or you can Click here to see another method for making a very simple electric motor.

**Step 2:** Using the information gathered in steps 1, study the factors that may affect the efficiency of an electric motor. Conduct an experiment to find the efficiency of a sample electric motor under various loads and report your findings. The efficiency, **e**, of a motor is traditionally defined as the ratio of power being generated to power being supplied:

**Note:** When we talk about the load in an electric motor or any thing else that can rotate, we are talking about the torque.

**What is torque?**

Torque is the ability of a force to produce a rotary_motion.

**Give me an example!**

Have you ever climbed a steep hill on a bicycle? Remember how much force you had to use to turn the pedals? That force was torque. It turned the crank that turned the sprockets that turned the wheels of the bicycle to produce rotary motion. It takes more torque to pedal uphill than downhill.

The Torque on an object about some pivot point is due to the action of a force on the object:

Torque = “Force” times the “Lever Arm”

So torque is the product of a force and its perpendicular distance from a point about which it causes rotation or torsion. The unit of torque is the newton meter, but you can also use other units such as kilogram meter or feet pound or gram centimeters. In all cases you have a force and a distance. The units of torque can be converted to each other. An on line conversion program is available at futek.com web site and another one at http://www.ex.ac.uk/cimt/dictunit/cctorq.htm.

### Question/ Purpose:

The purpose of this project is to learn about the electric motors and study the factors that may affect their efficiency.

A specific question that you are going to study in this project is:

How does the amount of load affect the efficiency of an electric motor?

**Why this question?**

We know that we can easily overload an electric motor to stop it from spinning. Such motor will continue to consume electricity and create heat while doing no work. At this time the efficiency of that motor is zero. In other words none of the electricity entered the motor will be converted to mechanical energy. This simple test shows that the efficiency of each electric motor is depended on the load, so load is one of our independent variables that can be studied for its effect on efficiency of an electric motor.

### Identify Variables:

When you think you know what variables may be involved, think about ways to change one at a time. If you change more than one at a time, you will not know what variable is causing your observation. Sometimes variables are linked and work together to cause something. At first, try to choose variables that you think act independently of each other.

Independent variable (also known as manipulated variable) is the amount of load.

Dependent variable is the efficiency of an electric motor.

Constants are input voltage, method and procedures.

Controlled variables are the room temperature and temperature of motor before each experiment.

### Hypothesis:

Based on your gathered information, make an educated guess about the effect of load on the efficiency of an electric motor. One possible Hypothesis is offered here:

The motor will have it’s highest efficiency while the load is half of the lowest load that can halt the motor. For example if a motor is not able to start with loads over 80 g-cm, then such motor will be most efficient with 40 g-cm load.

Note that the results of your experiment may have you to reject your hypothesis.

### Experiment Design:

Design an experiment to test each hypothesis. Make a step-by-step list of what you will do to answer each question. This list is called an experimental procedure. For an experiment to give answers you can trust, it must have a “control.” A control is an additional experimental trial or run. It is a separate experiment, done exactly like the others. The only difference is that no experimental variables are changed. A control is a neutral “reference point” for comparison that allows you to see what changing a variable does by comparing it to not changing anything. Dependable controls are sometimes very hard to develop. They can be the hardest part of a project. Without a control you cannot be sure that changing the variable causes your observations. A series of experiments that includes a control is called a “controlled experiment.”

### Procedure:

You must setup an experiment that uses a given motor to hoist a mass by coiling a string around its axle. Use a battery set or power supply that can produce a specific voltage across the motor. Due to the nature of the motor, the amount of current that is drawn will depend on the mass that is being hoisted. (Larger masses cause larger currents to be drawn.)

For the motor, the input power is supplied by electricity. The mechanical power that is generated creates a torque on the axle of the motor, and can be measured as the rate at which work is done in lifting a mass. In this case, power can be described as P=Fv where F is the applied force and v is the resulting velocity.

We are interested in determining the efficiency of a motor at loads of 10, 30 and 50 g-cm.

The work required to lift an object (at a constant speed) a certain height is equal to the force of gravity acting on the object (or weight) times the height that it is lifted. After being lifted to this height, this object stores the work done as gravitational potential energy. Therefore, the gravitational potential energy (PE) of an object at a given height from the ground is

**Potential Energy = mass * (acceleration of gravity) * height = mgh .**

For example if we use the motor to lift a 1 kg object to a height of 45 meters, the potential energy stored in the object at height 45 m is:

PE = mass * g * height = (1 kg) * (10 m/s2) * (45 m) = 450 J

Click Here to learn more about the potential energy. Also the acceleration of gravity is 9.8 m/s/s, but we used 10 instead to simplify our calculations.

Now you can calculate the electrical energy that was used to produce this potential energy. To do that you need to measure the voltage and current and the time the motor was on.

First you use the formula W=V.I to calculate how many watt of energy was being used at each moment. Then you multiply that by the time in seconds to calculate electrical energy based on Watt Seconds or Joule.

1 W-s = 1 Joule

For example think that you used a 12 volts battery to run the motor and the current while the motor was running was 0.1 amps and it took 500 seconds for the object to move that distance. Then W-s= 12 * 0.1 * 500 = 600 J

Since we want to test the efficiency of a motor at loads of 10, 30 and 50 g-cm, it is good if we simply use a shaft, axle or pulley with the diameter of 2 cm, so the radios will be one centimeter and as a result a 50 gram weight can be used to create 50 g-cm torque.

Special Considerations

1) How will you determine the velocity of the mass being lifted?

2) The force supplied by the motor cannot be measured directly. If a mass is hung

from the axle, under what conditions do you know what the tension in the

string is? Note that the force supplied by the motor is the tension in the string.

3) Make sure you do not operate the motor at voltages higher than it’s recommended voltage. Applying more voltage than what is recommended can damage your motor and affect your results.

4) Ideally, you want to produce a graphical output. How are you going to

incorporate multiple trials? What will you plot?

**Note:** As you see in the above diagram, you may also connect another volt-meter to the battery to read its voltage during the operation. This is specially needed if you are using a small battery. The voltage in small batteries drops under load.

You will not need this voltmeter if you are using a power supply that produces and maintains a fixed voltage.

**What is the control?**

When you change the load in this experiment and get different readings, you know that changes in your readings is caused by changes in the load; however, someone may doubt that and suggest that other unknown factors may have caused changes in your readings. That is why you may want to have another identical motor with all voltmeters and ammeters attached as your control.

**What do I do with my control?**

You do almost everything that you are doing with your test motor except changing the load. Since you are not changing the load, you just read the meters and record.

### Materials and Equipment:

Electric motor 1

Mounting unit (attaches motor to a stand) 1

Desk clamp and stand 1

Axle unit (for mounting a mass to hoisted) 1

String 1 roll

Masses and carriage for holding them 1 set

Meter tape or meter stick 1

Digital multimeters (that can measure current or voltage) 2

Power supply or battery 1

Connecting wires about 10 feet

Binding posts (for attaching multiple wires together) 2

Masking tape and duct tape 1 roll

### Results of Experiment (Observation):

Experiments are often done in series. A series of experiments can be done by changing one variable a different amount each time. A series of experiments is made up of separate experimental “runs.” During each run you make a measurement of how much the variable affected the system under study. For each run, a different amount of change in the variable is used. This produces a different amount of response in the system. You measure this response, or record data, in a table for this purpose. This is considered “raw data” since it has not been processed or interpreted yet. When raw data gets processed mathematically, for example, it becomes results.

Repeat the experiment with three different loads and report your findings.

**Some notes from my sample experiment:**

My first challenge was finding an electric motor. I was thinking of using an electric drill, but that required working with high AC voltage. AC voltage could create additional hazard and complications. I found a small electric fan (about $2.00) and removed the electric motor from that. I also bought a small battery holder that can hold two batteries.

Next, I needed to make some kind of spool.

I used wood glue and connected two corks to each other to form a spool.

I then tried to use this cork spool and a tread to lift something very light. It did not work. The diameter of spool is high, so any small weight can cause a high torque that can stop motor from turning.

I had to make a different spool with much less diameter.

To make the new spool, I opened an emptied pen and cut a piece of its inner tube. Then I made two circles from heavy construction paper that worked as flanges for my spool. The rod of electric motor could enter the tube (with some pressure) and hold it tightly.

For the weight, I used a small plastic bag that weighted 2 grams. For additional weights, I used small screws, 1.6 grams each.

I had a laboratory stand and a clamp that could hold the motor at the height of 5 feet (150 cm). I also had some wire leads that came handy.

Since I only had one multimeter, I had to repeat my measurements many times. For example I used the motor to lift the empty bag 3 times and I recorded the current. I did that 3 times and recorded the voltage (under load). I also did that 3 times and measured the time it takes for the bag to be lifted 5 feet.

I needed to have the voltage, current (Amps) and time in order to calculate the amount of electrical energy.

Calculation of the physical energy or potential energy is easy. For that, I only need to know the mass and the height (5 feet).

Picture in the right shows the main material that I used for my experiment. It does not show the laboratory stand and the scale that I used for weighting the plastic bag and screws

Following is my sample results table:

Lifted Object | Mass | lift time in seconds | Volts | Amps | Potential Energy | Electrical Energy in J |

Empty bag | 2 g | 1.5 s | 1.3 | 0.22 | 0.03 J | 0.429 Joule |

Bag+1 screw | 3.6 g | 1.9 s | 1.3 | 0.22 | 0.054 J | 0.543 J |

Bag+2 screws | 5.2 g | 2.3 s | 1.25 | 0.24 | 0.078 J | 0.690 J |

Bag+3 screws | 6.8 g | 2.7 s | 1.19 | 0.24 | 0.102 J | 0.725 J |

Bag+4 screws | 8.4 g | 5 s | 1.05 | 0.24 | 0.126 J | 1.26 J |

Bag+5 screws | 10 g | Failed | 0.7 | 0.25 | 0 | Unlimited |

**Remarks:** The voltage without load was 2.8 V.

To calculate electrical energy, I multiplied time (in seconds) by volts by Amps.

To calculate potential energy, I multiplied mass (in kilogram) by 10 (estimated acceleration of gravity) by height (in meters). 5 feet is 1.5 meter.

Finally I divided the potential energy by electrical energy to calculate the efficiency. (Table below).

Mass | Potential Energy | Electrical Energy in J | Efficiency |

2 g | 0.03 J | 0.429 Joule | 0.0699 |

3.6 g | 0.054 J | 0.543 J | 0.0994 |

5.2 g | 0.078 J | 0.690 J | 0.1130 |

6.8 g | 0.102 J | 0.725 J | 0.1406 |

8.4 g | 0.126 J | 1.26 J | 0.1 |

10 g | 0 | Unlimited | 0 |

The highest efficiency in my motor was for a load of 6.8 grams. The motor halted with 10 grams. Half of that is 5 grams. Based on my hypothesis, the highest efficiency is at 5 gram load (5 grams is half of the lowest load that can halt the motor). Based on the above results, I will reject my hypothesis.

Calculations:

Enter your calculations at this section.

### Summary of Results:

Summarize what happened. This can be in the form of a table of processed numerical data, or graphs. It could also be a written statement of what occurred during experiments.

It is from calculations using recorded data that tables and graphs are made. Studying tables and graphs, we can see trends that tell us how different variables cause our observations. Based on these trends, we can draw conclusions about the system under study. These conclusions help us confirm or deny our original hypothesis. Often, mathematical equations can be made from graphs. These equations allow us to predict how a change will affect the system without the need to do additional experiments. Advanced levels of experimental science rely heavily on graphical and mathematical analysis of data. At this level, science becomes even more interesting and powerful.

### Related Questions & Answers:

What you have learned may allow you to answer other questions. Many questions are related. Several new questions may have occurred to you while doing experiments. You may now be able to understand or verify things that you discovered when gathering information for the project. Questions lead to more questions, which lead to additional hypothesis that need to be tested.

### Possible Errors:

If you did not observe anything different than what happened with your control, the variable you changed may not affect the system you are investigating. If you did not observe a consistent, reproducible trend in your series of experimental runs there may be experimental errors affecting your results. The first thing to check is how you are making your measurements. Is the measurement method questionable or unreliable? Maybe you are reading a scale incorrectly, or maybe the measuring instrument is working erratically.

If you determine that experimental errors are influencing your results, carefully rethink the design of your experiments. Review each step of the procedure to find sources of potential errors. If possible, have a scientist review the procedure with you. Sometimes the designer of an experiment can miss the obvious.

### References:

Some reference are provided in the form of links in this project guide.

Most physics books contain information about energy and related calculations. Visit your local library and see a few. You may find very easy to understand books that will give you a jumpstart with this subject.

Additional web references are:

http://www.oneworld.org/energy/whatis.html

http://www.uwsp.edu/cnr/wcee/keep/Mod1/Whatis/energymeasures.htm