PS3+(9-11)+-+9

**Students demonstrate an understanding of forces and motion by…**

 __9a explaining through words, charts, diagrams, and models the effects of distance and the amount of mass on the gravitational force between objects (e.g. Universal Gravitation Law).__

 __9b using Newton’s Laws of Motion and the Law of Conservation of Momentum to predict the effect on the motion of objects__**.**

**Dave M. and Chris P.**

What do these GSEs mean? What subtopics do students need to address to understand these GSEs?

 * **Newton's Law of Universal Gravitation:** The law of gravitation is as follows




 * **Kepler's Laws of Planetary Motion:** Kepler's law fits in naturally with the discussion of Newton's Law of Universal Gravitation.
 * 1) All the planets orbit the sun in elliptical paths
 * 2) A planet sweeps out an equal area of space in an equal amount of time in its orbit.
 * 3) The ratio of the cube of a planet's mean distance from the Sun and the square of its period is a constant.


 * **Planetary Orbits:** Students should understand how gravity affects the orbits of the planets in our universe and how without gravity our universe would not be ordered the way it is. Students should be able to explain the direction of the planets and how they revolve around the sun.


 * **Astronomical Phenomena:** Teachers can use this opportunity to discuss many astronomical ideas that are related to the concept of gravity. An example of such a phenomena is the existence of seasons. Seasons occur because the earth is actually not a perfect circle. More mass is located around the equator making the earth slightly


 * **Gravitational Energy:** Teachers can also the idea of gravitational energy which is an extension of the idea of potential energy that they should have previously learned. Paired with the concept of conservation of energy students can determine **escape speeds** for satellites in earths orbit.


 * **Momentum:** Students should be introduced to the idea of momentum and should be able to apply the formula to real life situations.


 * **Conservation laws:** Students need to understand when momentum is conserved and when momentum is not conserved. These rules correspond to inelastic and elastic collisions.


 * **Elastic vs Inelastic Collisions:** When two objects collide elastically the total momentum is conserved. This is not the case in inelastic collisions. Students need to understand these differences.

What ideas to students need to understand before they can address the topics described above?

 * **3-D kinematics**
 * **Vectors**
 * **Mathematical Relationships:** Students must understand how variables in a given equation are related (inversely, linearly, etc) This will enable them to understand how the gravitational force will change when the variables to the main equation are changed.
 * **Newton's Laws of Motion:** Everything about Newton's laws of motion can still be applied when we venture farther away from the earth, the only difference is that we can't take g=9.8 m/s^2
 * **Velocity**
 * **Mass**
 * **Force**
 * **Net Force**
 * **Energy**
 * **Potential & Kinetic Energy**
 * **Energy Conservation:** Energy conservation is applicable in studying collisions and students must understand this principle before collisions can be analyzed.

What misconceptions are students likely to have about these topics?

 * 1) "9.81 m/s^2 is the acceleration due to gravity EVERYWHERE"! Most students don't understand or have never been taught that 9.81 is an approximation of the acceleration due to gravity and is only valid near the earth's surface. When problems arise that deals with satellites and other planetary objects that are a significant distance away from the earth this number is essentially meaningless.
 * 2) "Gravity is just the force that makes objects fall"! Most students don't understand that gravity is much more than just a force that causes objects to fall to earth's surface. They don't realize that gravity is the key force that keeps our universe in orbit; the force that keeps the planets orbiting around the sun rather than spiraling off into the oblivion.
 * 3) "Gravity is only relevant when we are talking about the earth and other planets". Students don't realize that gravitational forces exist between any two bodies. We are ALL gravitationally attracted to one another.
 * 4) "Heat and Sound are not forms of energy". When students analyze a collision, they understand that energy must be conserved and in the case of many inelastic collisions that are confused as to where the energy goes. They don't understand that if two cars collide, the energy of motion that the two cars had is converted into heat and sound which are forms of energy. Some energy is also used to deform the bodies of the two vehicles.

What phenomena and representations help students understand these topics?

 * Here is an explanation of vectors from [|Sixty Symbols] that includes a force demonstration: It is important for students to understand the nature of vectors and how many quantities within the subject of physics are vector quantities. The magnitude and direction of these quantities is essential in order to successfully complete problems that include such vector quantities. This video explains the idea of a vector and also refers to forces as vector quantities.

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Real world examples of collisions can be used to help students understand these concepts. Students learn about collisions in their physics classroom but there always seems to be a disconnect between the concepts that they learn and the ideas and schema about collisions that they already know and have created in the past. The following videos are great real world examples of inelastic collisions that will definitely get students motivated to explore and learn about collisions more in depth. Students know a lot about collisions before ever entering a physics classroom and these ideas need to be activated. These videos would be great ways to start a lesson and spark interest into the tasks for the day. media type="custom" key="10746662" align="center"


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Diagrams are also great representations that help students understand physical concepts. EVERY problem that students solve should be accompanied by a small diagram or sketch that illustrates what is happening. If students get in the habit of drawing a small diagram or constructing a free body diagram they engage in the process of trying to figure out exactly what is being asked of them. Many of the problems that involve Newton's law of gravitation are very complicated when written out but when they are drawn the problems simplify quite nicely. Teachers should help their students begin to be able to draw their own diagrams and decipher what is being asked of them in a given problem. An example of a free body diagram can be seen below:



What activities or activity sequences can be used to address these GSEs?

 * 1) Hands on investigations. Discovery learning is the best way for students to fully learn and understand physical concepts. There are many experiments that can be done involving elastic and inelastic collisions. Experimental apparatus is available that allows for the simulation of a seemingly frictionless surface (similar to an air hockey table) and excellent demonstrations can be done to investigate elastic collisions between pucks that hit at different angles. Using a slow motion video camera this can be analyzed quantitatively.
 * 2) Videos of collisions. Teachers can show students videos of different types of collisions and the class can slow down the video on the smart board and "draw" in the different forces that are at work. The collisions can then be analyzed and students can determine how much energy was lost and in what form.
 * 3) Students can create different videos of their own collisions and explain forces that are applied to each object.
 * 4) Real world applications about collisions and experiments to explain these. (An example would be giving a car crash example and using equations about collisions determining which vehicle it at fault.

Released NECAP items

 * NECAP 2009 GR 11 03