Use Proportionality and Inverse Variation to Describe Physical Laws Such As Hook's Law

Use proportionality and inverse variation to describe physical laws such as Hook's Law, Newton's Second Law of Motion, and Boyle's Law.

Use proportionality and inverse variation to describe physical laws such as Hook's Law, Newton's Second Law of Motion, and Boyle's Law.

Use

PROPORTIONALITY AND INVERSE VARIATION

Including, but not limited to:

• Direct variation –a linear relationship between two variables,x(independent) andy(dependent), that always has a constant, unchanged ratio,k, and can be represented byy=kx
• Characteristics of direct variation
• Linear proportional relationship
• Linear
• Passes through the origin (0, 0)
• Represented byy=kx
• Constant of proportionality represented as
• Whenb= 0iny=mx+b,thenk= the slope,m
• Ex:
  

• Inverse variation – a relationship between two variables,x(independent) andy(dependent), that always has a constant, unchanged ratio,k, and can be represented by
• Characteristics of inverse variation
• Proportional relationship
• Non-linear
• Does not pass through the origin (0, 0)
• Represented by
• Constant of proportionality represented as k=xy
• Ex:
  

To Describe

PHYSICAL LAWS SUCH AS HOOKE'S LAW, NEWTON'S SECOND LAW OF MOTION, AND BOYLE'S LAW

Including, but not limited to:

• Modeling physical laws through data collection and analysis
• Hooke’s Law – the force required to stretch or compress a spring a given distance is directly proportional to the distance. Hooke’s Law is represented byF = kx,whereFis the amount of force,kis the constant factor associated with the spring (stiffness), andxis the amount of displacement or change.
• Ex:
  
• Newton’s Second Law of Motion – the force required to move an object is directly proportional to the mass of the object and the acceleration desired. Newton’s Second Law of Motion is represented byFnet= ma,whereFnetis the net force,mis the mass of the object, andais the acceleration.
• Ex:
  
• Boyle’s Law – if temperature is constant, then pressure of an ideal gas is inversely related to the volume of the gas. Boyle’s Law is represented byPaVa= PbVb,wherePis the pressure on a volume of gas andVis the volume of the gas.
• Ex:
  

Note(s):

• Grade Level(s)
• Grade 8 studied direct variation and proportionality.
• Algebra I studied the linear parent functionf(x) =x.
• Mathematical Models with Applicationsintroduces application of inverse variation.
• Algebra II will study inverse variation and the rational function,f(x) =.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS
• I. Numeric Reasoning
• B1 – Perform computations with real and complex numbers.
• II. Algebraic reasoning
• B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
• VII. Functions
• A2 – Recognize and distinguish between different types of functions.
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
• X. Connections