How is physics useful in describing and analyzing collisions?
In this unit students examine collisions between objects. They observe several different collisions between objects of different masses moving at different speeds. Then students represent the motion of objects using measured values of distance and time, stroboscopic motion diagrams and graphs of distance vs. time and velocity vs. time in diagrams such as those produced by calculator based ranger (CBR) motion detector units. Next they examine the relationship between the impact time and impact force in a collision - what scientists call impulse. This leads to a discussion and eventual comparison of various safety devices such as seat belts, helmets, and airbags along with the physics principles behind them. Students then qualitatively relate the impulse of the objects in a collision to the mass of the objects and their resulting change in velocity. Lastly, students measure the speeds and calculate the momenta of different objects before and after a collision such as billiard balls or toy train cars. Then these momenta are analyzed, leading to a discussion of the measured differences in the before and after momenta and eventually the Law of Conservation of Momentum.
STANDARD P2: MOTION OF OBJECTS The universe is in a state of constant change. From small particles (electrons) to the large systems (galaxies) all things are in motion. Therefore, for students to understand the universe they must describe and represent various types of motion. Kinematics, the description of motion, always involves measurements of position and time. Students must describe the relationships between these quantities using mathematical statements, graphs, and motion maps. They use these representations as powerful tools to not only describe past motions but also predict future events.
P2.1 Position — Time
P2.1A Calculate the average speed of an object using the change of position and elapsed time.
P2.1B Represent the velocities for linear and circular motion using motion diagrams (arrows on strobe pictures).
P2.1C Create line graphs using measured values of position and elapsed time.
P2.1D Describe and analyze the motion that a position-time graph represents, given the graph.
P2.2A Distinguish between the variables of distance, displacement, speed, velocity, and acceleration.
P2.2B Use the change of speed and elapsed time to calculate the average acceleration for linear motion.
P2.2C Describe and analyze the motion that a velocity-time graph represents, given the graph.
P2.3x Frames of Reference
P2.3a Describe and compare the motion of an object using different reference frames.
P3.3A Identify the action and reaction force from examples of forces in everyday situations (e.g., book on a table, walking across the fl oor, pushing open a door).
P3.3b Predict how the change in velocity of a small mass compares to the change in velocity of a large mass when the objects interact (e.g., collide).
P3.3d Analyze why seat belts may be more important in autos than in buses.
P3.4 Forces and Acceleration
P3.4C Solve problems involving force, mass, and acceleration in linear motion (Newton's second law).
P3.4f Calculate the changes in velocity of a thrown or hit object during and after the time it is acted on by the force.
P3.4g Explain how the time of impact can affect the net force (e.g., air bags in cars, catching a ball).
P3.5a Apply conservation of momentum to solve simple collision problems.
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- How are the time of impact and the force related during a collision?
- How are the masses of the objects and the resulting changes in velocity related to each other in a collision?
- How does the total momentum before and after a collision relate to each other?
- How do technological devices such as seat belts, helmets, and air bags work to reduce injuries in a collision?
- How can the motions of the objects in a collision be represented and analyzed?
change in momentum (∆p = m∆v)
conservation of momentum
impulse (Ft = m∆v)
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