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Aim: How do we analyze relationships between variables?

Explore the different types of relationships between variables in physics equations, including linear, non-linear, parabolic, hyperbolic, and inverse squared relationships. Practice calculating slopes and identifying the relationships between force, mass, speed, and radius in centripetal and gravitational force equations.

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Aim: How do we analyze relationships between variables?

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  1. Aim: How do we analyze relationships between variables? Homework: For each of the four types of relationships, find a physics equation that demonstrates that relationship and state which variables show that relationship

  2. Linear Relationship Two variables y and x are linearly related if they can be written in the form of an equation, y = mx +b (m is the slope and b is the y-intercept- the value of y when the line crosses the x-axis)

  3. Non-linear relationships There are a few types of non-linear relationships that we need to know: • Parabolic (or Quadratic) • Hyperbolic (or Inverse) • Inverse Squared

  4. Parabolic (Quadratic) Relationships Two variables x and y are in parabolic relationship if they can be expressed by an equation of the form y =ax2 + bx + c

  5. Hyperbolic (Inverse) Relationship Two variables x and y are in a hyperbolic relationship if they can be expressed in the form y = a/x.

  6. Inverse Square Relationship Two variables x and y are in an inverse square relationship if they can be expressed in the form, y = a/x2

  7. Linear or Non-linear? Write down the equations. State whether x and y are linearly or non-linearly related. If non-linear, state what type of non-linear relationship. 1. y = 6x 2. y = 2/x 3. y = 10 + 4x2 4. x2y2 = 23 5. 3y = 2x + 7 6. 44y = 3/x2 7. y = 0.5x + z 8. y1/2 = 8x + 8 9. 15x = 20y

  8. Application to Physics: The Centripetal Force Fc = centripetal force r= radius v = speed of object m = mass of object Fc= (m v2)/r According to this equation, what is the relationship between? i)Force and mass ii) Force and speed of object iii) Force and radius of circular motion

  9. Application to Physics: The Gravitational Force • Linear or Non-Linear? • Gravitational Force and mass • b) Gravitational force and radial distance between the masses

  10. Practice calculating slope of a line The slope of a line measures its steepness. The formula we use to calculate slope is slope = rise/run

  11. Practice Problem 1: Find the slope This line goes through both of these points, (6,0) and (9,2) Slope = ???

  12. Practice Problem 2: Find the slope Slope = ???

  13. Practice Problem 3: Find the slope of a line that goes through points (4,7) and (2,11) Write the equation of this line.

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