Collisions Teacher Guide
Unit
Collisions
Subject
Physics
Grade Level
HS
Activity Name(s)
Elastic Collisions
Forces  Equal and Opposite
Heating by Hitting
Hit the Wall
Being Prepared
Students could do these activities individually, but setup and performance of the activities would be more easily facilitated by groups of 2 or 3.
In "Heating by Hitting," remind students to watch their fingers and heads when releasing the weights.
Getting Started
Carefully read and follow instructions of use of temperature sensors and force probes.
In "Forces  Equal and Opposite," Collect Data III, a rubber stopper works well as a small object to push toward the other sensor.
Suggested Timeline
Pretest and post tests will each take 10 to 15 min. approximately.
Each activity will take 1 to 2 class periods of 45 min.
Thinking about the Discovery Questions
This unit deals with the idea of conservation of motion and energy. Forces always occur in equal pairs with opposite directions. When you kick a football you apply a force to the ball, but the ball also applies an equal force in the opposite directions to to your foot. An applied force can cause motion through a distance. When an object moves, potential energy can be converted to kinetic energy or vice versa. Energy of motion (kinetic) can become thermal (heat) energy due to friction that occurs when 2 objects are in contact, or when they collide.
Misconceptions
A common misconception students hold is that equal and opposite forces are on the same object, rather than different objects. They also forget that although forces are equal, if the masses are unequal, the accelerations of the objects will also be different. The more massive the object the smaller its acceleration. For example when a semitruck collides with a car going the same speed, after the collision the car will move faster than the truck due to their mass differences.
Learning Objectives
 NGSS
 Performance Expectations
 HSPS21. 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.
 HSPS22. 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.
 HSPS32. Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative positions of particles (objects).
 HSPS33. Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.
 Disciplinary Core Ideas
 HSPS2: Motion and Stability: Forces and Interactions
 PS2.A: Forces and Motion
 Newton’s second law accurately predicts changes in the motion of macroscopic objects. (HSPS21)
 Momentum is defined for a particular frame of reference; it is the mass times the velocity of the object. In any system, total momentum is always conserved. (HSPS22)
 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. (HSPS22),(HSPS23)
 PS2.A: Forces and Motion
 HSPS3: Energy
 PS3.A: Definitions of Energy
 Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms. (HSPS31),(HSPS32)
 At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. (HSPS32) (HSPS33)
 These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as either motions of particles or energy stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space. (HS PS32)
 PS3.D: Energy in Chemical Processes and Everyday Life
 Although energy cannot be destroyed, it can be converted to less useful forms—for example, to thermal energy in the surrounding environment. (HSPS33),(HSPS34)
 PS3.A: Definitions of Energy
 HSPS2: Motion and Stability: Forces and Interactions
 Practices
 Developing and using models
 Develop or modify a model  based on evidence  to match what happens if a variable or component of a system is changed.
 Analyzing and interpreting data
 Using mathematics and computational thinking
 Use mathematical representations to describe and/or support scientific conclusions and design solutions.
 Apply mathematical concepts and/or processes (e.g., ratio, rate, percent, basic operations, simple algebra) to scientific and engineering questions and problems.
 Constructing explanations and designing solutions
 Apply scientific ideas, principles, and/or evidence to construct, revise and/or use an explanation for real world phenomena, examples, or events.
 Developing and using models
 Cross Cutting Concepts
 Systems and system models
 Students can understand that systems may interact with other systems; they may have subsystems and be a part of larger complex systems. They can use models to represent systems and their interactions — such as inputs, processes and outputs — and energy, matter, and information flows within systems. They can also learn that models are limited in that they only represent certain aspects of the system under study.
 Energy and matter: Flows, cycles, and conservation
 Students learn matter is conserved because atoms are conserved in physical and chemical processes. They also learn within a natural or designed system, the transfer of energy drives the motion and/or cycling of matter. Energy may take different forms (e.g. energy in fields, thermal energy, energy of motion). The transfer of energy can be tracked as energy flows through a designed or natural system.
 Systems and system models
 Performance Expectations
 NSES
 NSES Physical Science – Motions and forces
 Whenever one object exerts force on another, a force equal in magnitude and opposite in direction is exerted on the first object.
 NSES Physical Science – Conservation of energy and the increase in disorder
 Heat consists of random motion and the vibrations of atoms, molecules, and ions. The higher the temperature, the greater the atomic or molecular motion.
 Energy can be transferred by collisions in chemical and nuclear reactions, by light waves and other radiations, and in many other ways. However, it can never be destroyed. As these transfers occur, the matter involved becomes steadily less organized.
 NSES Physical Science – Motions and forces
Discussion: Setting the Stage
With a Newton's Cradle, asked students to predict what will happen when different numbers of balls are released. If one ball is released, one ball on the end will move, with 2 balls, 2 will move, and so on, since the energy of the system must be conserved.
Why do the balls eventually stop moving? Where did their energy go? Students should recognize that energy is lost as the heat of friction, resulting in the loss of energy & motion.
Discussion: Formative Questions
Elastic Collisions

Why do the atoms initially approach and then move away from one another? How is energy transferred from 1 atom to another?
The red kinetic energy is transferred from one atom to another during collisions of the atoms. Atoms initially attract one another because the negatively charged electron cloud of one atom is attracted to the positively charged nucleus of the other atom. When atoms are very close or touch, the negatively charged electron clouds of both atoms repel each other, pushing the atoms apart. In a closed system, the atoms continually attract and repel each other, depending on their distance apart, so the atoms would normally be in continual motion. If they struck with the right orientation and sufficient energy, theoretically, the atoms could form covalent bonds and stick together. The total sum of kinetic and potential energy remains constant for the closed system.
Heating by Hitting

If the height of the drop for the weight, or the weight itself, is increased, what would you expect to happen to the temperature change?
Since the potential energy of the weight is increased the temperature change of the hit should increase.
Discussion: Wrapping Up

How do rockets travel in space, if there are no particles to push against? How do rockets change direction in space?
Students frequently think that when rockets launch they travel upward because they push against the ground, when in actuality, escaping gases from the rocket thrusters create a force, and the rocket moves in the opposite direction as a result.
Additional Background
Newton's Law state that for every action force, there is an equal and opposite reaction force. Students sometimes forget that these forces act on different objects. Since force is equal to mass x acceleration, it is possible to set the mass x the acceleration of one object equal to the mass x acceleration of the other object. See http://www.physicsclassroom.com/class/newtlaws/u2l4a.cfm
Analysis
Elastic Collisions

How does kinetic energy, potential energy, and total energy change when two atoms collide?
The sum of kinetic and potential energy = a constant total energy Kinetic energy is converted to potential energy and vice versa, while total energy stays the same under ideal conditions

When do the atoms have the greatest kinetic energy?
When the atoms are as close together as possible but before they repel each other; however their kinetic energies are equal but opposite in direction.

What happens when you move the balls before starting?
They immediately move back closer together.

What happens when you run the model with one or more additional atoms?
The total energy of the system remains the same, but is transferred back and forth among the atoms as they collide.

Why does the kinetic energy (red color) move from one atom to the next?
Kinetic energy is transferred from one atom to the next as they collide.

Review the following description of the collisions: "As one gets close to the next, it pushes on it, moving it. But the second pushes back on the first, slowing it. As the second moves away, the forces reduce until the first is stopped and the second is going as fast as the first." How does this explain the energy involved in an elastic collision? Be prepared to share your answer with the class.
In the elastic collisions of atoms, the opposite charges of the electron cloud and the nucleus of the different atoms attract the atoms together, accelerating them towards each other. When the atoms are too close the negative charges of the electron clouds of both atoms repel one another, accelerating the atoms away from one another.
Forces  Equal and Opposite

Compare the graphs from the two force sensors. Describe how the action force and the reaction force are related for each of the experiments that you tried.
The action force should be equal and opposite to one another.

If a small car crashes into a large truck that isn't moving, which vehicle experiences more force?
The forces on the car and truck are equal but opposite in direction. Since the truck has the larger mass, it will have a smaller acceleration than the car.

How does Newton's Third Law apply to rockets?
As the gases rush out of the rocket in one direction, the rocket is accelerated in the opposite direction. Mass x acceleration of the gases = mass x acceleration of the rocket. The force on the gas is equal and opposite in direction to the force on the rocket.

How does Newton's Third Law apply to a seesaw?
The mass x the acceleration on one side equals the mass x the acceleration of the opposite side. The smaller mass will have the larger acceleration.
Heating by Hitting

How much did the temperature change, on average, for each hit?
Student answers will vary with their data, but may be quite small.

Calculate the gravitational potential energy of the weight that it had when you released it. Note that the height is measured in meters.
PE = m * g * Δh where PE = potential energy (Joules), m = mass (kilograms), g = acceleration of gravity = 9.8 m/s*s, and Δh = change in height (m).

PE = m * g * Δh where PE = potential energy (Joules), m = mass (kilograms), g = acceleration of gravity = 9.8 m/s*s, and Δh = change in height (m). Calculate the heat energy that was gained by the clay per hit.
Student answers may vary if they changed the mass used or height of the release.

E = m * C * (ΔT) where E = Energy (Joules), m = mass (kilograms), C = heat capacity of modeling clay = 1700 Joules/kg ΔC, and (approximate) (ΔT) = change in temperature ( °C ). How do these two amounts of energy compare? If they are not the same, why not?
The two calculations should be the same, but some energy may be lost to the surroundings.

Calculate the percentage of the potential energy (PE) that you were able to detect as heat energy.
% PE =[ ( Potential Energy gained by the clay  Potential Energy lost by the weight) / Potential Energy gained by the clay ] x 100

Compare your results with the results of other groups. Theoretically, if the weight stopped moving when it hit the clay, all of the energy in the weight would end up as heat in the clay. Discuss how you might improve your experiment to measure the full amount of heat that is generated by the collision.
Student answers may vary, but may involve some way to insulate the system so there is less heat loss to the air and surroundings.
Hitting the Wall

Kinetic energy is related to an object's speed and mass. Ball A has a mass of 1 kg and a speed of 10 m/s. Ball B is traveling at the same speed (10 m/s) and has a mass of 2 kg. What is the difference in kinetic energy between Ball A and Ball B?
Kinetic Energy ( KE) = 1/2 mass x velocity squared. KE of ball A = 1/2 x 1 kg x (10 m/s x 10 m/s) = 50 kg m/s. KE of ball B = 1/2 x 2 kg x (10 m/s x 10 m/s)= 100 kg m/s. Ball B has twice the KE of ball A

In a collision, the kinetic energy of the hammer changes into kinetic energy of the molecules. What is different about these two forms of kinetic energy?
The molecules of the hammer have an average velocity for the entire object in one direction, while the molecules of clay are vibrating individually in many different directions.

If you rub a penny very energetically, it will heat up. How is that process similar to the model of the hammer? How is it different?
It is similar in that a force is being applied to the penny as pushes or pulls on the penny's atoms. It is different in that the hammer's force is from gravity while the rubbing produces frictional forces.

Which would you say is more correct? The temperature is proportional to the velocity (momentum of the hammer). The temperature is proportional to the square of the velocity (energy of the hammer).Explain your reasoning.
Students should find the energy gained by the clay is closer using the square of the velocity.
Further Investigation
Have the students predict and design their own invetigations by changing the height, mass of the weight, or number of spheres, etc. to investigate further extensions with both the sensors and models.