The Arizona STEM Acceleration Project

Meter Stick Balance Practicum.

Meter Stick Balance Practicum

A Middle and High School STEM lesson

Author:

Rich McNamara

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Date:

05/28/2024

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Notes for teachers

There are two versions of the Assessment:

• Easy version:

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• Advanced version:

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List of Materials

• Meter Stick Balance Sets for each lab group including:
• Meter Sticks
• Balance stands
• Easy version: 2 Mass Hangers. �Advanced : Just 1 mass hanger
• A Set of Labeled Mass to assign to each group.
• A Set of unknown masses for each group.
• An electronic or triple beam balance to measure the mass of the meter sticks or unknown objects.

Standards

Science:

Essential HS.P3U1.6:

• Collect, analyze, and interpret data regarding the change in motion of an object or system in one dimension, to construct an explanation using Newton’s Laws.

Plus HS+Phy.P3U1.3

• Develop a mathematical model, using Newton’s laws, to predict the motion of an object or system in two dimensions (projectile and circular motion).

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Standards

Math:

A2.A-CED.A: Create equations that describe numbers or relationships.

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• A2.A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include problem-solving opportunities utilizing real-world context. Focus on equations and inequalities arising from linear, quadratic, rational, and exponential functions.

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• A2.A-REI.B Solve equations and inequalities in one variable. A2.A-REI.B.4 Fluently solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Objective(s):

Easy Version:

By the end of class today, I will be able to apply the equation for a balance (developed from the distance vs. mass investigation) to determine the mass of an unknown.

Advanced Version:

By the end of class today, I will be able to apply the equation for a balance (developed from the distance vs mass investigation) to determine the mass of a meter stick.

Agenda (lesson time)

0 to 5 min:

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5 to 15 min:

15 to 30 min:

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30 to 40 min:

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40 to 45 min:

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45 to 50 min:

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Explain the expectations for the practicum.

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Students collect and set up their equipment.

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Collect data and solve for the unknown value.

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Bring their unknown mass or meterstick to the testing station.

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Students determine the percentage difference between the prediction and the actual mass value.

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Students return their equipment to the staging area.

Intro/Driving Question/Opening

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Can we use the model of an inverse relationship to make predictions?

Can we determine the mass of an object using the balance equation?

You can use earn extra credit bases on the percentage difference between their prediction and the measured values.

Hands-on Activity Instructions

This formative assessment activity should come after students have sufficient experience using the following equation:

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m₁d₁ = m₂d₂

where

m₁ represents the mass on the left.

d₁ represent the distance of mass 1 from the fulcrum

m₂ represents the mass on the right.

d₂ represent the distance of mass 2 from the fulcrum

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m₁ m₂

< —- d₁—---><---------d₂—----->

Hands-on Activity Instructions

Step by step instructions

• Normal Version:
• Remove the mass hangers from both sides of the meterstick.
• Adjust the position of the fulcrum/pivot point until the meter stick is balanced.
• Add the mass hangers and the known and unknown mass and adjust their positions until the meterstick is balanced again.
• Use the measured values of d ₁, d₂ and the known mass to determine the value of the unknown mass. Images may be helpful to show how things are setup.

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m₁ m₂

< —- d₁—---><---------d₂—----->

Hands-on Activity Instructions

Step by step instructions

• Advanced version:
• Remove the mass hangers from both sides of the meterstick.
• Adjust the position of the fulcrum/pivot point until the meter stick is balanced.
• Record the position of the meter stick’s center of mass.
• Add a single mass hangers to the meterstick.
• Slide the meterstick to the left or right of fulcrum/pivot until the meterstick is balanced.
• Use the measured values of d ₁, d₂ and the known mass to determine the value of the unknown mass. Images may be helpful to show how things are setup

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B is the mass hanger.

C is the new balance point.

G is the meter stick’s center of mass.

Assessment

Students will complete a 20pt Practicum Write Up:

5pts - PURPOSE Statement: Using a meter stick balance to determine the mass of an unknown.

5pts - Diagram and Data: Diagram of the set up with each of following items labeled:

• including the fulcrum,
• the meterstick,
• each of the masses and
• distances from the fulcrum.

5pts - Solve for the unknown mass (from equation to the value with units)

5pts - Actual value & percent difference from your prediction.

Differentiation

Basic Version for struggling students:

• The position of the unknown mass is easily identified making it easier to record values and calculate the prediction.
• Use this PhET Simulation: Balancing Act. to review the relationships between mass & lever arm.

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Advanced Version:

• The students must first determine the meter sticks center of mass.
• They must then recognize that they have to shift the meter stick to the left of before placing the mass hanger to rebalance the meter stick

Remediation

Extension/Enrichment

Basic Version: �Encourage students to change the position of each of the masses and see how well the new prediction compares to the original prediction. ��

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Advanced Version:

Reposition the fulcrum and see how well the new prediction compares the the original predictions.