Unit – Newton’s Laws of Motion Keith Newman Joshua Ball Joseph Guzzi Topic – Using Atwood Machines with Newton’s Laws Grade Level – 8th Grade Objective(s): Students will be able to: • Apply the principles of Newton's Second Law of Motion by formulating mathematical equations and solving problems involving and using Atwood Machines. • Measure, calculate, and interpret data collected with use of a sonic ranger and data logging program to explain how other forces within a closed system effect the acceleration of an object. National Standard(s): Content Standard B - MOTIONS AND FORCES • • • The motion of an object can be described by its position, direction of motion, and speed. That motion can be measured and represented on a graph. An object that is not being subjected to a force will continue to move at a constant speed and in a straight line. If more than one force acts on an object along a straight line, then the forces will reinforce or cancel one another, depending on their direction and magnitude. Unbalanced forces will cause changes in the speed or direction of an object's motion. PA Standard(s): • 3.1.7 D Identify change as a variable in describing natural and physical systems o Describe scale as a form of ratio and apply to a life situation • 3.1.10 E Describe patterns of change in nature, physical and man made systems o Describe how fundamental science and technology concepts are used to solve practical problems. o Describe the effects of error in measurements • 3.4.10 C Distinguish among the principles of force and motion o Know Newton’s Laws of Motion (including inertia, action and reaction) and gravity and apply them to solve problems related to forces and mass. Connection(s): By applying Newton’s Laws of Motion to real life scenarios and demonstrating how things work, students can observe and appreciate the usefulness that pulleys have (i.e. increasing pulleys decreases the amount of force needed to lift objects). Students will gain the ability to determine direction and magnitude of forces as well as see the real-world application of Newton’s Second Law and how it pertains to everyday life. The labs application to Newton’s Law will allow students to be able to explain Newton’s Law in scientific language. Background/Prior Knowledge: • • Students have already learned Newton’s Laws of Motion and are able to solve simple onedimensional force problems. Students have knowledge of using the Sonic Ranger and data logging program in terms of interpreting distance, velocity, and acceleration values calculated by said program. Material(s): • • • • • • Atwood Machines Masses PowerPoint notes Handout (follow along) Lock and marker for demonstration Atwood Lab Sheet Sonic Ranger Day 1 (60 minute period) Objective(s): • Students will be able to draw a free body diagram to represent scenarios. • Students will be able to translate a free body diagram into an equation. Start-up Activity: • • • Students will be directed to pick up notes handout from front table as they enter the room. Students will begin writing down a brief summary of Newton’s three laws of motion and write down the formula for how force is determined in terms of mass and acceleration on the top of their notes handout page. Teacher will begin class by having students share their responses to the start-up activity as a pre-assessment. Anticipatory Set (Lead – In) - (10 minutes) • Teacher directed review of one dimensional motion accompanied with small group brainstorming using PowerPoint (slides 1-3). Mini-Demonstration (s) (15min) • Teacher demonstrates force using “pushing” scenarios shown below; show multiple scenarios of how forces affect different objects based on the acceleration the object experiences. The following scenarios are introduced to students for discussion in the groups. A. Vehicle scenario – Students are to compare a situation in which cars of different weights and traveling at different speeds will do to each other when they impact each other (different locations, i.e. sides, back end, front end, parked and moving). Students are to assume the vehicles are made of the same materials. B. Contact between people – Students will take various scenarios of human contact (i.e. high five, running into each other, one standing still the other moving) and compare and predict what would happen based upon their previous knowledge. C. Cannon scenario – Students will make predictions about a situation with a cannon firing different projectiles at a wall made of various different materials. • Teacher will revisit Newton’s Second Law of motion in relation to vertical motion by presenting demonstrations involving falling objects; compare falling book to falling marker. Have students discuss which object produces more force and why (greater the mass, the greater the force, provided acceleration is constant). If students need further clarification, connect this to the real word by asking which one they would rather have dropped on their foot. Mini – Lesson (25 min) • Review a vertical force problem (object fixed to a point with no movement) with PowerPoint (slides 4-5), reiterate free body diagrams and process of determining the net forces that act on an object. Students will create free body diagram on notes handout in conjuncture with PowerPoint. Assist students in completing a free body diagram by monitoring and prompting opened questions. (Do you think the object will move? How do you know? What does the movement tell you about the net force acting on the object?) Atwood Machine PowerPoint: Situation 1: (slides 6-9) Demonstrate different scenario 1 using Atwood machine with discussion and Power Point handout activity. Walk students through the steps of solving a force problem involving the Atwood Machine. Prompt students to assist in solving the problem by using ideas/concepts presented earlier in the lesson Atwood Machine PowerPoint: Situation 2: (slides 10-16) In small groups, students will use the notes handout sheet to solve steps 1 and 2 of situation 2. Have students present their free-body diagrams to teacher before moving on to step 2. Students who have completed step 2 may go on to step three after teacher verification. All students should work on completing situation 2 for homework. Wrap - Up: • With 3-5 minutes left in class, teacher will reiterate how to solve Atwood Machine problems by asking students to verbally share the steps in analyzing and solving a problem. Teacher will remind students to complete situation 2 for homework. Modification for time: If class is unable to complete force body diagrams for Situation 2 then students will only be required to complete the diagrams fro homework. Modification for readiness: Teacher will clarify that all free body diagrams for the lesson are the same and students may refer to the previous situation in the handout in order to make drawing. If majority of the class has difficulty creating formulas for the net forces students may instead qualitatively describe the forces involved in the situation. Based on qualitative responses teacher will decide either to proceed by providing the formulas for the student or have students continue to work on creating formulas. Day 2 (90 minute Lab period) Objectives: • Students will be able to demonstrate scenarios using an Atwood machine. • Students will be able to create a mathematical model to explain motion in and Atwood machine using technology (Sonic Ranger and data logging equipment). • Students will be able to demonstrate their understanding by presenting both oral and written research on applications of pulleys. Prior to class (10 Minutes) • Setup lab areas for Atwood Lab work. Start Up • Students will take out their note sheets and homework from previous class. Students are to share and discuss their solutions with their table partners. Intro • (10 Minutes) (10 minutes) Review previous day’s scenarios (homework) in conjunction with the Atwood machine. Student groups collaborate and brainstorm with free body diagrams and calculate net forces. Pre-Lab (5 minutes) • • Lab • • • Students will get into their lab groups (lab groups are pre-assigned and are based on input from the math department so that each group has at least one member that is capable of making the necessary calculations while other members will perform the research portion) and will be instructed on proper use of the Atwood machine in correlation with sonic ranger and data logging program. Students are instructed to complete the data collection portion only and to save the calculation portion for the second half of class (This helps to insure that all groups have had ample time to perform the data collection). (30 minutes) Groups will perform lab activity using Atwood machines to derive qualitative scales for the movement of the system (i.e. slow, slower, medium, fast, faster, etc…). The role of the teacher during this time frame is to be a facilitator and troubleshooter assisting students in the set up and proper technique of using the Atwood machine in combination with the data logging equipment.(i.e. Keeping arms away from Sonic Ranger) Students that have finished their data collection will be permitted to return to their desks and to begin calculating the accelerations of each system. Closure (10 minutes) • When all students have completed data collection, teacher will display transparency of the free body diagrams for each situation and discuss assumptions and results. Teacher will review the mathematical computations for the first part of the lab. Student’s lab results will then be used to connect the concept of acceleration of the system and how it can be calculated. • The teacher will assign the following assessment. Assessment (30 minutes) • Students that are capable will be required to perform the calculations for net force and acceleration for each Atwood system. Students that are not capable will be assigned the task of researching the use of pulleys and write a one paragraph composition that illustrates real world applications of pulleys. All students will share their responses with each other and the class on day three. Day 3 (60 minute period) Objectives: Students will be able to discuss applications of the Atwood machine (pulley systems) and the impact of Newton’s 2nd Law in their lives. Start up (20 minutes) • Students will reassemble their lab groups and will identify what they think are their strengths and weaknesses in their presentations. Review Lab results, have students share their concerns and questions with the rest of the class. Encourage students to respond to each other to flow the classroom discussion. Modification- Pose question to students “How can we turn our weaknesses into strengths”? Assignment Reflection (10 minutes) • Lab Reflections, students will write a few sentences or paragraph discussing how other students helped or assisted them in their lab. Pose meta-cognitive questions to the students, “What do you think you would use a pulley for?” “Why is this Lab assignment important to you?” Wrap-up (30 minutes) • • Extend and discuss real-world applications of pulleys. Have students share their research on pulleys. Ask students how they have seen or used pulleys in their life. Using the PowerPoint presentation the teacher will show a basic two pulley system and how it reduces the force required to lift an object by half its weight. A crane and sail boat will be referenced. Extension(s): Do more pulleys help us?