Mechanics - NYCNYS Science Resources for Teaching and PD



Mechanics

|Aim: |Major Understanding |Performance Objective; |Activities and |Stan-dards |

| | |Students will be able to: |Real World Application: | |

|Why is direction important? |1a Measured quantities can be classified as |-Compare and contrast distance and |Teacher shows story on overhead detailing a |S4a; |

| |either vector or scalar |displacement |trip taken by a person. Hand out graph paper |S5a,S5b, |

| | |-Define the terms vector and scalar |and have students plot the various legs of the|S5c,S5f; |

| | | |trip. Have students determine, based on their|S6a,S6c; |

| | | |graph, the total distance traveled and the |S7d,S7e; |

| | | |distance from starting point to ending point |S8c |

| | | |of the trip | |

|How is motion described? |1d An object in linear motion may travel with|-Construct and interpret graphs of position, |Using a model car, a meter stick and a stop |S1d,S1f; |

| |a constant velocity or with acceleration |velocity or acceleration versus time |watch, students will record the various |S2c,S2f; |

| | |-Determine and interpret slopes and areas of |variables associated with the motion of the |S4a; |

| | |motion graphs |car. Students should mark a starting position|S5a,S5b, |

| | |-Determine that motion is relative to the |and label it “0 meter”. Then they should set |S5c,S5f; |

| | |observer |the car into motion and measure the distance |S6a,S6c,S6e; |

| | |-Distinguish between speed and velocity |traveled as well as time the motion. Using |S7d,S7e; |

| | | |the data they collected, the students should |S8a,S8c |

| | | |be able to plot a graph of change in distance | |

| | | |vs. change in time, calculating the slope of | |

| | | |that graph (which will be the speed) and | |

| | | |noting the shape of the graph. | |

|Aim: |Major Understanding |Performance Objective; |Activities and |Stan-dards |

| | |Students will be able to: |Real World Application: | |

|How may concurrent forces by combined |1c The resultant of two or more vectors, |-Determine the resultant of two or more |-Attach 2 ropes to 1 object and have 2 |S1d; |

|graphically and algebraically? |acting at any angle, is determined by vector |vectors graphically or algebraically |students pull at the ropes at a 90( angle. |S4a; |

| |addition |-Apply the parallelogram method to find the |Have the class predict which way the object |S5a,S5b,S5c, |

| | |resultant of any two vectors |will move. |S5d,S5e,S5f; |

| | |-Construct and label proper vector diagrams |-Hand out clues to a treasure hunt. Each clue|S6a,S6b,S6c, |

| | |-Draw scaled diagrams, using a ruler and |should have the magnitude and direction (NSEW)|S6d,S6e; |

| | |protractor |that needs to be followed. Each group should |S7a,S7b,S7d, |

| | | |graphically recreate the clues, using “due” |S7e; |

| | | |for horizontal or vertical directions, and 45(|S8a,S8c |

| | | |for combination directions. Teacher can use | |

| | | |other angles, as well, for protractor | |

| | | |practice. Have students determine the | |

| | | |displacement of the treasure from the starting| |

| | | |point. No matter what order the clues were | |

| | | |followed, the displacement should be the same.| |

| | | |Have students explain why. | |

|How are vectors like babies? |1b A vector may be resolved into |-Resolve a vector into perpendicular |-Demonstrate how vectors are analogous to |S1d; |

| |perpendicular components |components: graphically and algebraically |babies in the sense that just as every baby |S2b,S2c; |

| | |-Apply the parallelogram method in reverse to |came from a mother and a father, every vector |S4a,S4b; |

| | |find the perpendicular components |can be formed from a pair of perpendicular |S5a,S5b, |

| | |-Draw scaled diagrams, using a ruler and a |components, no matter what angle from the |S5c,S5e, S5f; |

| | |protractor |horizontal or vertical the vector is directed.|S6a,S6d; S7d; |

| | |-Relate trigonometry to solving for the |-Review the Pythagorean Theorem, as well as |S8c |

| | |components |sine, cosine and tangent functions to show how| |

| | | |the components can be mathematically | |

| | | |calculated. | |

|Aim: |Major Understanding |Performance Objective; |Activities and |Stan-dards |

| | |Students will be able to: |Real World Application: | |

|How are cliff divers and baseballs related? |1e An object in free fall accelerates due to |-Demonstrate the independence of the |Assign students into small groups where they |S1d; |

| |the force of gravity. Friction and other |horizontal and vertical components of motion |will provide examples of both types of |S4a,S4b; |

| |forces cause the actual motion of a falling |-Compare the motion of projectiles launched at|projectile motion, explaining what happens in |S5a,S5b, |

| |object to deviate from its theoretical motion.|an angle to that of projectiles launched |both directions complete with vector diagrams |S5c,S5d, |

| |(Note: Initial velocities of objects in free |horizontally |and path sketches, and link the projectile |S5e,S5f; |

| |fall may be in any direction.) |-Relate projectile motion to linear and free |motion to both linear and free fall motion. |S6a,S6b, |

| |1g A projectile’s time of flight is dependent|fall motion | |S6c,S6d, S6e; |

| |upon the vertical components of its motion | | |S7a,S7b, |

| |1h The horizontal displacement of a projectile| | |S7d,S7e; |

| |is dependent upon the horizontal component of | | |S8a,S8b,S8c |

| |its motion and its time of flight | | | |

|Why is it so hard to move a boulder? |1i According to Newton’s First Law, the |-Compare and contrast Aristotle’s and |-Have set up in front of the classroom a |S1a,S1b, S1d; |

| |inertia of an object is directly proportional |Galileo’s ideas of motion |quarter set on an index card, which is |S2c,S2d, S2f; |

| |to its mass. An object remains at rest or |-Explain how Newton’s concept of inertia |covering a beaker. Challenge any student in |S4a,S4b; |

| |moves with constant velocity, unless acted |improved upon their laws |the class to get the quarter to drop into the |S5a,S5b, |

| |upon by an unbalanced force. |-Distinguish between mass and weight |beaker without moving the quarter. Swiftly |S5c,S5d, |

| | |-Demonstrate the relationship between mass and|and horizontally pull the card. Why did the |S5e,S5f; |

| | |inertia |quarter drop into the glass? Lead into a |S6a,S6d, S6e; |

| | | |discussion about force and friction. |S7b,S7d, S7e; |

| | | |-Have the class stand up with their hands up. |S8a,S8c |

| | | |Explain that they’re on a subway that is | |

| | | |entering the station. Next, tell them that | |

| | | |the train has arrived and have them act out | |

| | | |their motion as the train comes to a halt. | |

| | | |Why did they all jerk forward even though the | |

| | | |train stopped? Why are they thrown against | |

| | | |the door of the car when it makes a sharp turn| |

| | | |in the other direction? Why should all cars | |

| | | |be equipped with neck/head rest and seat | |

| | | |belts? | |

|Aim: |Major Understanding |Performance Objective; |Activities and |Standards |

| | |Students will be able to: |Real World Application: | |

|What variables determine whether an object |1k According to Newton’s Second Law, an |-Verify Newton’s Second Law for linear motion |-Provide groups of students with objects that |S1b,S1d; S2d; |

|will accelerate? |unbalanced force causes a mass to accelerate |-Reason the relationship between mass and |occupy the same shape and volume but different|S4a,S4b; |

| | |acceleration |masses. Ask each group to exert the same |S5a,S5b, |

| | |-Apply the mathematical principle that governs|amount of force on each object and observe the|S5c,S5d, |

| | |the mass-acceleration relationship by deriving|motion of each object. Which one moved |S5e,S5f; |

| | |the formula: F=ma |faster, and why? Repeat, but apply differing |S6a,S6b, |

| | | |forces to the objects and record observations.|S6c,S6d, S6e; |

| | | |What relationship exists between mass, force |S7a,S7b, |

| | | |and acceleration? |S7d,S7e; |

| | | | |S8a,S8c |

|How can a person be weightless but not |1l Weight is the gravitational force with |-Determine the acceleration due to gravity |Ask students to observe an inertia ball with |S1b,S1d; |

|massless? |which a planet attracts a mass. The mass of |near the surface of the Earth |string tied on both ends. Is the tension |S4a,S4b; |

| |an object is independent of the gravitational |-Analyze why mass as a scalar quantity and |greater in the upper or lower string? Which |S5a,S5b, |

| |field in which it is located. |weight is a vector quantity |property is important in the upper string |S5c,S5d, |

| | | |(mass or weight)? If the string is instead |S5e,S5f; |

| | | |snapped downward, have students predict which |S6a,S6d; |

| | | |string would be more likely to break. Which |S7b,S7d, S7e; |

| | | |property is important in the lower string? |S8a,S8c |

|What are the different types of friction? |1o Kinetic friction is a force that opposes |-Use vector diagrams to analyze mechanical |-Ask students to describe what would happen to|S1b,S1d; |

| |motion |systems (equilibrium and nonequilibrium) |an object if the force of friction equaled the|S4a,S4b; |

| | |-Determine the coefficient of friction for two|applied force on an object |S5a,S5b, |

| | |surfaces |-Provide groups of students with 3 set ups: |S5c,S5d, |

| | |-Relate friction to the normal force |wood to slide across the desk; a cylindrical |S5e,S5f; |

| | | |object to roll across the desk; and a |S6a,S6b, |

| | | |graduated cylinder filled with water and a |S6c,S6d, S6e; |

| | | |marble to drop in it. Have the students |S7a,S7b, |

| | | |observe the motion of each set up and explain |S7d,S7e; |

| | | |the interactions taking place between the |S8a,S8b, S8c |

| | | |surfaces in contact | |

|Aim: |Major Understanding |Performance Objective; |Activities and |Stan-dards |

| | |Students will be able to: |Real World Application: | |

|Why is follow through important? |1pThe impulse imparted to an object causes a |-Define momentum |-Have 2 students hold a bed sheet up in the |S1b,S1d; |

| |change in its momentum |-Distinguish between impulse and change in |front of the classroom. Challenge students to|S4a,S4b; |

| | |momentum |throw a raw egg as fast as they can at the |S5a,S5b, |

| | | |sheet without breaking it If one should hit |S5c,S5d, |

| | | |the wall, ask why that one broke but the |S5e,S5f; |

| | | |others that hit the sheet did not? |S6a,S6b, |

| | | |-Ask students why they might see big, yellow |S6c,S6d, S6e; |

| | | |rubber cans near highway exit ramps, or why it|S7a,S7b, |

| | | |hurts less to fall on a carpeted floor instead|S7d,S7e; |

| | | |of on a hard wood floor? |S8a,S8b, S8c |

|Why do rockets take off? |1q According to Newton’s Third Law, forces |-Explain how forces interact |-Provide groups of students with 1 straw, 1 |S1b,S1d; |

| |occur in action/reaction pairs. When one |-Distinguish between action and reaction |balloon, string and tape and ask them to |S2c,S2d; |

| |object exerts a force on a second, the second |forces |construct a rocket that can fly across the |S4a,S4b; |

| |exerts a force on the first that is equal in |-Show how action/reaction pairs do not cancel |room. Why did the balloon propel across the |S5a,S5b, |

| |magnitude and opposite in direction. |out |room? |S5c,S5d, |

| | | |-Have students push their hands against the |S5e,S5f; |

| | | |edge of their desks. Have students slam their|S6a,S6b, |

| | | |hand against the desk. What evidence is there|S6c,S6d, |

| | | |to show that a force was exerted against their|S6e;S7a,S7b,S7d|

| | | |hand? |,S7e;S8a, S8b, |

| | | | |S8c |

|Why is a pool hall a good place to study |1r Momentum is conserved in a closed system |-Verify conservation of momentum |Set up an air track with 2 cars on it. Ask |S1b,S1d; |

|momentum? |(Note: Testing will be limited to momentum in |-Distinguish between elastic and inelastic |volunteers to demonstrate 3 different types of|S4a,S4b; S5a, |

| |one dimension) |collisions |collisions: one car hitting a car at rest, a |S5b, S5c, S5d, |

| | | |car hitting another car moving in same |S5e,S5f; |

| | | |direction, and the two cars moving towards |S6a,S6b, |

| | | |each other in opposite directions. Before |S6c,S6d,S6e |

| | | |each collision, ask class to predict both the |S7a,S7b,S7d,S7e|

| | | |approximate change in velocity (faster, |; S8a,S8b, S8c |

| | | |slower, same) and direction (same, opposite) | |

|Aim: |Major Understanding |Performance Objective; |Activities and |Stan-dards |

| | |Students will be able to: |Real World Application: | |

|How are mass and gravity related? |1t Gravitational forces are only attractive, |-Describe Newton’s Law of Universal |Ask students what keeps the moon in orbit |S1b,S1d; |

| |whereas electrical and magnetic forces can be |Gravitation |around the Earth, and the planets orbiting the|S3c,S3d; |

| |attractive or repulsive |-Describe gravitational field strength |Sun? |S4a,S4b; |

| |1u The inverse square law applies to | | |S5a,S5b, |

| |electrical and gravitational fields produced | |-rwa- |S5c,S5d |

| |by point sources | |Assign a class project to explore different | |

| |1s Field strength and direction are determined| |planetary systems explaining forces and | |

| |using a suitable test particle (Notes: 1) | |factors that maintain them in constellation. | |

| |Calculations are limited to electrostatic and | | | |

| |gravitational fields. 2)The gravitational | |Plan a trip to the Museum of Natural history | |

| |field near the surface of the Earth and the | |to visit the new Hayden Planetarium. | |

| |electrical field between two oppositely | |Connect to for | |

| |charged parallel plates are treated as | |offers to science and engineering educational | |

| |uniform.) | |community connection. | |

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Key Idea: (5) Energy and matter interact through forces that result in changes in motion.

Performance Indicator: (5.1) Students can explain and predict different patterns of motion of objects (e.g., linear and uniform circular motion, velocity and acceleration, momentum and inertia).

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