written by
Peter Bohacek
published by
the Science Education Resource Center

This high-resolution video lets students explore conservation of momentum in a cannon-pendulum system. A small metal ball is fired from a pneumatic cannon into a sticky surface of a weighted pendulum. Students can measure the position and time for the ball after it is launched (but before it hits the pendulum) and the swing angle of the pendulum after the ball strikes it. Mass of the marble and the pendulum apparatus are given. Learners will determine the momentum of the steel ball before it hits the pendulum to predict the maximum swing angle.

Direct Measurement Videos allow students to easily analyze physical situations encountered in introductory mechanics courses. Features include digital rulers, frame-counters, and other screen overlays for making precise measurements. Video can be streamed or viewed in stepped motion to analyze frame-by-frame action. This material is part of Pedagogy in Action, a library of resources for educators provided by SERC, the Science Education Resource Center.

Please note that this resource requires
Quicktime.

Motion and Stability: Forces and Interactions (HS-PS2)

Students who demonstrate understanding can: (9-12)

Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. (HS-PS2-1)

Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system. (HS-PS2-2)

Disciplinary Core Ideas (K-12)

Forces and Motion (PS2.A)

Newton's second law accurately predicts changes in the motion of macroscopic objects. (9-12)

If a system interacts with objects outside itself, the total momentum of the system can change; however, any such change is balanced by changes in the momentum of objects outside the system. (9-12)

Crosscutting Concepts (K-12)

Systems and System Models (K-12)

When investigating or describing a system, the boundaries and initial conditions of the system need to be defined. (9-12)

NGSS Science and Engineering Practices (K-12)

Analyzing and Interpreting Data (K-12)

Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data. (9-12)

Analyze data using computational models in order to make valid and reliable scientific claims. (9-12)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

Use mathematical or computational representations of phenomena to describe explanations. (9-12)

NGSS Nature of Science Standards (K-12)

Analyzing and Interpreting Data (K-12)

Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data. (9-12)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

AAAS Benchmark Alignments (2008 Version)

2. The Nature of Mathematics

2B. Mathematics, Science, and Technology

9-12: 2B/H3. Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments.

4. The Physical Setting

4F. Motion

9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

9-12: 4F/H4. Whenever one thing exerts a force on another, an equal amount of force is exerted back on it.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

12. Habits of Mind

12B. Computation and Estimation

9-12: 12B/H2. Find answers to real-world problems by substituting numerical values in simple algebraic formulas and check the answer by reviewing the steps of the calculation and by judging whether the answer is reasonable.

9-12: 12B/H3. Make up and write out simple algorithms for solving real-world problems that take several steps.

9-12: 12B/H9. Consider the possible effects of measurement errors on calculations.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

MP.6 Attend to precision.

High School — Algebra (9-12)

Seeing Structure in Expressions (9-12)

A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

Creating Equations^{?} (9-12)

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Reasoning with Equations and Inequalities (9-12)

A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Linear, Quadratic, and Exponential Models^{?} (9-12)

F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F-LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

P. Bohacek, Direct Measurement Video: Ballistic Pendulum, (Science Education Resource Center, Northfield, 2013), <https://serc.carleton.edu/dmvideos/videos/ballistic_pendu.html>.

Bohacek, P. (2013, February 9). Direct Measurement Video: Ballistic Pendulum. Retrieved December 16, 2017, from Science Education Resource Center: https://serc.carleton.edu/dmvideos/videos/ballistic_pendu.html

Bohacek, Peter. Direct Measurement Video: Ballistic Pendulum. Northfield: Science Education Resource Center, February 9, 2013. https://serc.carleton.edu/dmvideos/videos/ballistic_pendu.html (accessed 16 December 2017).

%0 Electronic Source %A Bohacek, Peter %D February 9, 2013 %T Direct Measurement Video: Ballistic Pendulum %I Science Education Resource Center %V 2017 %N 16 December 2017 %8 February 9, 2013 %9 video/quicktime %U https://serc.carleton.edu/dmvideos/videos/ballistic_pendu.html

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