To explore particle trajectories, try this simulation of firing various objects out of a cannon. You can find out how the angle, initial speed, mass, and air resistance affect the path of the projectile. This item is part of a larger collection of simulations developed by the Physics Education Technology project (PhET).
The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. (6-8)
Newton's second law accurately predicts changes in the motion of macroscopic objects. (9-12)
Crosscutting Concepts (K-12)
Scale, Proportion, and Quantity (3-12)
Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth). (9-12)
Systems and System Models (K-12)
Models can be used to represent systems and their interactions. (6-8)
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)
Developing and Using Models (K-12)
Modeling in 6–8 builds on K–5 and progresses to developing, using and revising models to describe, test, and predict more abstract phenomena and design systems. (6-8)
Develop and use a model to describe phenomena. (6-8)
Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)
Use a model to provide mechanistic accounts of phenomena. (9-12)
AAAS Benchmark Alignments (2008 Version)
4. The Physical Setting
6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.
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/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.
11. Common Themes
6-8: 11B/M1. Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly. They are also used for processes that are too vast, too complex, or too dangerous to study.
9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.
Common Core State Standards for Mathematics Alignments
Standards for Mathematical Practice (K-12)
MP.2 Reason abstractly and quantitatively.
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.
%0 Electronic Source %D March 3, 2006 %T PhET Simulation: Projectile Motion %I PhET %V 2023 %N 1 October 2023 %8 March 3, 2006 %9 application/flash %U https://phet.colorado.edu/en/simulation/projectile-motion
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