Chen Zhanjiang, Tan Wei Lin

Chen ZhanjiangTan Wei LinQCP 521 Teaching of Physics IIInteractive Simulation29 Nov 2010

Simulation for Principle of Moments

Class: Sec 3 Express

Topic: Principle of Moments

Specific Instructional Objectives

Students should be able to:1. Induce that for rotational equilibrium to be achieved in a beam-pivot system, the sum of the

product of the weight and distance to pivot for individual objects is the same for both sides of the pivot (principle of moments) from observation of pattern

2. Describe moments of an object as the tendency for it to rotate due to an applied force3. Deduce the unknown weight of an object by using the principle of moments in a beam-pivot

system

Prior Knowledge1. Units of measurement2. Weight = Mass x gravitational acceleration. Gravitational acceleration is taken to be 10 m/s2.3. Force can be interpreted as a push or pull. 4. Newton’s First and Second law.

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Chen Zhanjiang, Tan Wei Lin

Rationale for Using SimulationThe discovery of the Principle of Moments is carried out through a classic experiment, where the beam is balanced by objects on both sides, with the pivot at the centre. This inquiry-based approach could be difficult to achieve in real life as the process of measuring the weight of the object and adjusting the distance-from-pivot could be very tedious and time consuming. There would also be a large margin of error expected as it could be difficult to determine of the exact point of equilibrium due to factors such as wind speed and the steadiness of students’ hands when releasing the beam. These factors play an important role because the balanced beam is an unstable equilibrium. There are also systematic errors such as the uniformity of the weight of the ruler.

The simulation allows the students to “physically” adjust the positions of the objects while observing the works of the Principle of Moments. Coupled with a properly designed worksheet, the process of discovery would be much faster.

This simulation is also very appealing due to the cute cartoon characters, and more importantly the user-friendliness. The learning curve for this simulation is gentle and the students would be able to pick it up easily.

Other concepts could also be taught using this simulation, such as the Newton’s Third Law. The beam in the simulation has weight and it would be evident to the students when there is instability when the pivot is moved away from the centre of the beam. The concept of rotational equilibrium could also be linked to translational equilibrium, with the aid if Newton’s Third Law.

Activity for StudentsThe students will be directed to the following website for the simulation (Refer Appendix A for screenshots):

http :// fairlysimple . com / applets /05 TurningForces . html

The students are also required to open an Excel Spreadsheet, which would be a guided worksheet for them to work on (Refer attached Excel Spreadsheet). The spreadsheet is protected with a password and students will only be allowed to key in values at the appropriate cells.

The spreadsheet has 4 parts in total.

Part 1: Students will be guided to describe motion of the beam as a rotational motion in the clockwise or anti-clockwise direction. Guidance will be in the form of feedback, given to the various student responses.

Part 2A: This is a warm-up activity to get students started on Part 2B.

Part 2B: In this activity, students will be tasked to find the conditions for the beam to be balanced. Two quantities are given, namely, the sum, and the product, of the object’s weight and its distance

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Chen Zhanjiang, Tan Wei Lin

from the pivot (D.F.P.). Students will observe that the product must be equal (within a margin of error) on both sides of the beam for the beam to be balanced.

Part 3: This part builds on the previous to guide students to think about what the product actually means. Eventually, it is meant to show that the product, which is termed moments about a point, is the tendency to rotate.

Part 4: This is a question to test student’s ability to apply knowledge. Making use of the principle of moments, the weights of the two unknown masses will have to be found.

Other Possible Activities for Students1. The position of the pivot in this simulation can also be changed. In this way, weight of the

beam can also be used as a problem.2. The force diagram for the beam and objects could be drawn and discussed. The concept of

Newton’s Third Law could be discussed at the pivot. It could also be shown that the condition for translational equilibrium is also achieved in this case.

Improvements to the Simulation1. Use the quantity “weight of the objects”, expressed in Newtons, instead of displaying the

“mass” in kilogram. This is to allow easier extension to the relationship of moments as the turning effect of a force.

2. Allow the distance of the object from the pivot to be keyed in manually3. Exaggerate the imbalance of the beam so that it would be more obvious to emphasize that

the beam is not in equilibrium. Currently, the point of balance can only be determined by the feedback from the system. It is not obvious visually.

4. Allow the weight of the object to be changed5. Allow selection of the characters. This is especially important if the students want to go back

to the website any other time (after navigating away from it) to check the answers of their worksheet.

6. More significant figures should be used for numerical calculations in the simulation. Currently the results for the clockwise and anti-clockwise moments are only equal to 2 significant figures. Although the error is less than 1% (according to the sample answers), it may still be difficult for students to be convinced of the equality. However, this disadvantage can be used to drive home the learning point that most of the time, scientists make discoveries based on trends and if the error is in an acceptable margin, the principle can still be considered true.

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Chen Zhanjiang, Tan Wei Lin

Other simulations for principle of moments

http :// physics . bu . edu /~ duffy / java / Equilibrium 2. html This simulation is much more rigid compared to the current simulation chosen since the objects cannot be dragged. The distances have to be adjusted on a scale outside the diagram.

In addition, the results do not show visually. For example, the beam does not tip over when a resultant moment is created. It can only be shown numerically as a negative force at the support. Students might find it hard to grasp the idea of the negative forces at the supports, creating confusion.

http :// www . walter - fendt . de / ph 14 e / lever . htm This simulation is simpler but not as visually appealing. In addition, the calculations for the moments are shown. Therefore, it cannot be used for students to discover the special meaning about the product for themselves.

However, this simulation is also helpful because it uses weights instead of masses. The distances are also clearly marked out, thus, it is more systematic and has a much smaller error margin.

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Chen Zhanjiang, Tan Wei Lin

Appendix A - Screenshots of Simulation

Screenshot 1 – Default

The characters that appear in the simulation are randomly chosen from a larger data base. The screenshot above shows one of the possible default settings a student would observe.

Screenshot 2 – Taking the reading

The mass and distance from pivot (D.F.P) of the character could be read off the simulation by moving the mouse over the character.

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Chen Zhanjiang, Tan Wei Lin

Screenshot 3 – Unbalanced beam

The above image was captured while attempting Part 2B of the worksheet. The character on the right was being moved in an attempt to balance the beam. Although visually, the beam looks quite “horizontal”; however, the system prompts the user that the beam is not balanced. Upon receiving this response, students would have to continue to adjust the D.F.P of the character on the right to achieve equilibrium.

Screenshot 4 - Equilibrium

When equilibrium is achieved, the system prompts the user by congratulating the user. Upon receiving this response from the simulation, the student can then carry on and record the mass and D.F.P of the characters in the Excel worksheet.

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Chen Zhanjiang, Tan Wei Lin

Screenshot 5 – Finding the unknown

The above screenshot was taken while trying to determine the unknown mass of the character on the left (Part 4). Either one or two characters could be used to determine the unknown mass of the character as shown. Once an “equilibrium” response is obtained, the readings could be obtained and recorded in the Excel worksheet and the unknown mass could be calculated easily.

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