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B3 Momentum Key Question: How Well Is Momentum Conserved in Collisions?

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B3 Momentum Key Question: How Well Is Momentum Conserved in Collisions? INVESTIGATION B3 Collaborative Learning This investigation is Exploros-enabled for tablets. See page xiii for details. B3 Momentum Key Question: How well is momentum conserved in collisions? The law of conservation of momentum is the second of Materials for each group the great conservation laws in physics, after the law of y Colliding pendulum kit conservation of energy. In this investigation, students observe elastic collisions between balls of the same and y Physics stand* differing masses. The speed of each ball before and after y Two photogates* each collision is determined, and the total momentum y DataCollector* before and after each collision is calculated. Students y Calculator* compare the total momentum before and after each collision to determine how well momentum is conserved. y Balance or digital scale, accurate to 1 gram (for the class)* Learning Goals *provided by the teacher ✔ Perform elastic collisions between balls of various masses. Online Resources Available at curiosityplace.com ✔ Calculate the velocity and momentum of the balls before and after each collision. y Equipment Video: Colliding Pendulum y Skill and Practice Sheets ✔ Determine whether momentum is conserved in each collision. y Whiteboard Resources y Animation: Changes in Momentum GETTING STARTED y Science Content Video: Newton’s Third Law y Student Reading: Newton’s Third Law and Momentum Time 100 minutes Setup and Materials 1. Make copies of investigation sheets for students. 2. Watch the equipment video. 3. Review all safety procedures with students. NGSS Connection This investigation builds conceptual understanding and skills for the following performance expectation. HS-PS2-2. 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. Science and Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Using Mathematics and Computational Thinking PS2.A: Forces and Motion Systems and System Models Colliding Pendulum 41 MOMENTUM Vocabulary on each object’s mass. The higher an object’s mass, the collision – occurs when two or more objects hit more force it takes to deflect its motion. each other There are two types of collisions: elastic and inelastic. elastic collision – a collision in which the total kinetic When an elastic collision occurs, objects bounce off energy remains the same before and after the collision each other with no loss in the total kinetic energy of the inelastic collision – a collision in which the total kinetic system. The total kinetic energy before the collision is the energy after the collision is less than it was before the same as the total kinetic energy after the collision. The collision, and which usually involves objects sticking collision between billiard balls is very close to a perfectly- together or changing shape elastic collision. law of conservation of momentum – states that in the In an inelastic collision, objects change shape or absence of external forces, the total momentum of a stick together, and the total kinetic energy of the system remains constant system decreases. The energy is not destroyed, but it is momentum – the mass of an object multiplied by transformed into forms other than kinetic energy, such as its velocity a permanent change in shape, or sound, or heat. An egg Newton’s second law – states that acceleration is force hitting the floor is one example of an inelastic collision; divided by mass two vehicles colliding is another. In both cases, some of Newton’s third law – states that for every action force, the kinetic energy in the system permanently changes an there is a reaction force equal in strength and opposite object’s shape. in direction Momentum is a property of moving matter that depends on both mass and velocity. Momentum BACKGROUND describes the tendency of objects to keep going in the same direction with the same speed. One way to look at force is that force is the action that changes momentum. A collision occurs when two or more objects hit each Conversely, any change in momentum must create force. other, and the objects exert forces on each other. Newton’s third law tells us that any time two objects hit Momentum is the product of an object’s mass and each other, the forces exerted by the objects are equal velocity. The greater an object’s momentum, the harder in magnitude and opposite in direction. However, the it is to stop. A train car moving at even a very slow speed effect of the collision on each object can differ. During is difficult to stop because its momentum is large due to a collision, momentum and energy are transferred from its mass. one object to another. The law of conservation of momentum says the total Newton’s second law explains why colliding objects momentum in a system of interacting objects cannot react differently. The second law states that an object’s change as long as all forces act only between the acceleration is directly objects in the system. If interacting objects in a system proportional to the are not acted on by outside forces, the total amount of force exerted on the momentum in the system cannot change. If one object object and inversely gains momentum, the other loses the same amount, proportional to the leaving the total unchanged. object’s mass. The force Conservation of momentum can be used to determine felt by two colliding an unknown velocity or mass if all of the other masses objects is the same, but and velocities in the collision are known. It is important to the resulting acceleration include the direction of the velocity (positive or negative) and velocity depend because velocity and momentum are vector quantities. 42 B3 5E LESSON PLAN Engage Newton’s third law tells us that when two objects collide, they exert equal and opposite forces on each other. However, the effect of the force is not always the same. Demonstrate by rolling two balls of different mass Science Content Video Animation toward each other so they collide. Use two balls with a Newton’s Third Law Changes in Momentum significant difference in mass, such as a tennis ball and a baseball, or a ping pong ball and a golf ball. The force on each during the collision is the same, but they do not Elaborate have the same change in motion after the collision. Automakers use When studying motion related to collisions, we crash test dummies can predict how two colliding objects might move to study the effects using momentum and Newton’s third law of motion. of collisions on Momentum is the mass of an object multiplied by its passengers. Crash velocity. Because of this, you could also call it “mass test dummies contain in motion.” electronic sensors to measure the forces and accelerations Explore exerted at various Have students complete Investigation B3, Momentum. places on the body. The dummies are expensive, costing Students observe elastic collisions between balls of the more than $100,000 each, but they are also sturdy and same and differing masses. The speed of each ball before last through years of crash testing. and after each collision is determined, and the total momentum before and after each collision is calculated. Results of these tests have been used to make changes Students compare the total momentum before and in automobile design. The use of seat belts and airbags after each collision to determine how well momentum reduces the force on passengers by slowing down the is conserved. transfer of momentum, making today’s cars much safer than their predecessors. Explain Consider having students study the momentum, force, Revisit the Key Question to give students an opportunity and energy changes that are inflicted on a crash test to reflect on their learning experience and verbalize dummy and how those forces can be mitigated with understandings about the science concepts explored in safety devices in an automobile. the investigation. Curiosityplace.com resources, including student readings, videos, animations, and whiteboard Evaluate resources, as well as readings from your current science y During the investigation, use the checkpoint textbook, are other tools to facilitate student questions as opportunities for ongoing assessment. communication about new ideas. y After completing the investigation, have students answer the assessment questions on the Evaluate student sheet to check understanding of the concepts presented. Colliding Pendulum 43 MOMENTUM Explore INVESTIGATION B3 Guiding the INVESTIGATION Name ____________________________________________ Date ________________________ Setting up the experiment B3 Momentum Materials: ✔ Colliding pendulum kit If you wish to complete the investigation in a How well is momentum conserved in collisions? ✔ Physics stand shorter period of time, you can partially set up the This investigation is about momentum, a property of moving matter. An object’s ✔ Two photogates momentum depends on its velocity and mass. When a collision occurs between ✔ DataCollector equipment by attaching a hanger and arc to each two objects, momentum is transferred from one to the other. If no outside forces (such as friction) are present, the total momentum of the objects before the ✔ Calculator physics stand ahead of time. Then, during class, collision is the same as the total after the collision. ✔ Balance or digital scale, accurate to 1 gram In this investigation, you will observe collisions between objects of varying students will only have to attach and align the masses. You will calculate the momentum before and after each collision to determine how well the collisions follow the law of conservation of momentum. projectile and target balls to the correct height. Setting up the experiment The steel balls connect to the hanger by threading The colliding pendulum apparatus allows you to observe collisions between two balls of the same or different mass. The balls are made the strings through the holes in the two posts.
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