### Standards

#### Massachusetts Frameworks (2006):

**1.4** Interpret and apply Newton’s three laws of motion.

**1.5** Use a free-body force diagram to show forces acting on a system consisting of a pair of interacting objects. For a diagram with only co-linear forces, determine the net force acting on a system and between the objects.

**1.6** Distinguish qualitatively between static and kinetic friction, and describe their effects on the motion of objects.

**1.7** Describe Newton’s law of universal gravitation in terms of the attraction between two objects, their masses, and the distance between them.

#### Next Generation Science Standards:

**HS-PS2-1**. 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.

**HS-PS2-3**. Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision.

**HS-PS2-4**. Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.

#### AP Physics 1 Learning Objectives:

**1.C.1.1:** The student is able to design an experiment for collecting data to determine the relationship between the net force exerted on an object its inertial mass and its acceleration. [**SP 4.2**]

**1.C.3.1:** The student is able to design a plan for collecting data to measure gravitational mass and to measure inertial mass and to distinguish between the two experiments. [**SP 4.2**]

**2.B.1.1:** The student is able to apply to calculate the gravitational force on an object with mass m in a gravitational field of strength g in the context of the effects of a net force on objects and systems. [**SP 2.2, 7.2**]

**2.B.2.1:** The student is able to apply to calculate the gravitational field due to an object with mass M, where the field is a vector directed toward the center of the object of mass M. [**SP 2.2**]

**2.B.2.2:** The student is able to approximate a numerical value of the gravitational field (g) near the surface of an object from its radius and mass relative to those of the Earth or other reference objects. [**SP 2.2**]

**3.A.2.1:** The student is able to represent forces in diagrams or mathematically using appropriately labeled vectors with magnitude, direction, and units during the analysis of a situation. [**SP 1.1**]

**3.A.3.1:** The student is able to analyze a scenario and make claims (develop arguments, justify assertions) about the forces exerted on an object by other objects for different types of forces or components of forces. [**SP 6.4, 7.2**]

**3.A.3.2:** The student is able to challenge a claim that an object can exert a force on itself. [**SP 6.1**]

**3.A.3.3:** The student is able to describe a force as an interaction between two objects and identify both objects for any force. [**SP 1.4**]

**3.A.4.1:** The student is able to construct explanations of physical situations involving the interaction of bodies using Newton’s third law and the representation of action-reaction pairs of forces. [**SP 1.4, 6.2**]

**3.A.4.2:** The student is able to use Newton’s third law to make claims and predictions about the action-reaction pairs of forces when two objects interact. [**SP 6.4, 7.2**]

**3.A.4.3:** The student is able to analyze situations involving interactions among several objects by using free-body diagrams that include the application of Newton’s third law to identify forces. [**SP 1.4**]

**3.B.1.1:** The student is able to predict the motion of an object subject to forces exerted by several objects using an application of Newton’s second law in a variety of physical situations with acceleration in one dimension. [**SP 6.4, 7.2**]

**3.B.1.2:** The student is able to design a plan to collect and analyze data for motion (static, constant, or accelerating) from force measurements and carry out an analysis to determine the relationship between the net force and the vector sum of the individual forces. [**SP 4.2, 5.1**]

**3.B.1.3:** The student is able to re-express a free-body diagram representation into a mathematical representation and solve the mathematical representation for the acceleration of the object. [**SP 1.5, 2.2**]

**3.B.2.1:** The student is able to create and use free-body diagrams to analyze physical situations to solve problems with motion qualitatively and quantitatively. [**SP 1.1, 1.4, 2.2**]

**3.C.1.1:** The student is able to use Newton’s law of gravitation to calculate the gravitational force the two objects exert on each other and use that force in contexts other than orbital motion. [**SP 2.2**]

**3.C.1.2:** The student is able to use Newton’s law of gravitation to calculate the gravitational force between two objects and use that force in contexts involving orbital motion [**SP 2.2**]

**3.C.2.2:** The student is able to connect the concepts of gravitational force and electric force to compare similarities and differences between the forces. [**SP 7.2**]

**3.C.4.1:** The student is able to make claims about various contact forces between objects based on the microscopic cause of those forces. [**SP 6.1**]

**3.C.4.2:** The student is able to explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and that they therefore have certain directions. [**SP 6.2**]

**3.G.1.1**: The student is able to articulate situations when the gravitational force is the dominant force and when the electromagnetic, weak, and strong forces can be ignored. [**SP 7.1**]

4.A.1.1: The student is able to use representations of the center of mass of an isolated two-object system to analyze the motion of the system qualitatively and semi-quantitatively. [**SP 1.2, 1.4, 2.3, 6.4**]

**4.A.2.1:** The student is able to make predictions about the motion of a system based on the fact that acceleration is equal to the change in velocity per unit time, and velocity is equal to the change in position per unit time. [**SP 6.4**]

**4.A.2.2:** The student is able to evaluate using given data whether all the forces on a system or whether all the parts of a system have been identified. [**SP 5.3**]

**4.A.2.3:** The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity, and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. [**SP 1.4, 2.2**]

**4.A.3.1:** The student is able to apply Newton’s second law to systems to calculate the change in the center-of-mass velocity when an external force is exerted on the system. [**SP 2.2**]

**4.A.3.2:** The student is able to use visual or mathematical representations of the forces between objects in a system to predict whether or not there will be a change in the center-of-mass velocity of that system. [**SP 1.4**]

#### Concepts assessed on the SAT Physics Subject Test:

**Dynamics**, such as force, Newton’s laws, statics, and friction.
**Gravity**, such as the law of gravitation, orbits, and Kepler’s laws.

- What are Forces?
- Types of Forces
- Newton’s Laws
- Problem Solving With Newton’s Laws
- Pulleys
- Inclined Planes
- Newton’s Law of Universal Gravitation
- Weightlessness