Podcast
Questions and Answers
What does it mean when two variables are directly proportional?
What does it mean when two variables are directly proportional?
- If one variable increases, the other remains constant.
- Both variables increase or decrease together. (correct)
- If one variable increases, the other decreases.
- One variable changes independently of the other.
In an inversely proportional relationship, what happens to the dependent variable if the independent variable is tripled?
In an inversely proportional relationship, what happens to the dependent variable if the independent variable is tripled?
- It remains unchanged.
- It is decreased to one third of its original value. (correct)
- It is halved.
- It is increased by a factor of three.
What is the equation representing a variable directly proportional to the square of another variable?
What is the equation representing a variable directly proportional to the square of another variable?
- y = kx^3
- y = kx^2 (correct)
- y = k/x
- y = kx
If the normal force is decreased by a factor of three, what will happen to the force of friction?
If the normal force is decreased by a factor of three, what will happen to the force of friction?
Which of these best explains the meaning of the constant of proportionality (k)?
Which of these best explains the meaning of the constant of proportionality (k)?
How would the acceleration change if the mass is increased by a factor of five, assuming constant net force?
How would the acceleration change if the mass is increased by a factor of five, assuming constant net force?
What does the symbol ∝ signify in a relationship between two variables?
What does the symbol ∝ signify in a relationship between two variables?
Which of the following statements is true about direct proportionality?
Which of the following statements is true about direct proportionality?
What happens to the kinetic energy if the velocity of an object is tripled?
What happens to the kinetic energy if the velocity of an object is tripled?
If the separation distance in a gravitational force equation is increased by a factor of 10, how does this affect the force?
If the separation distance in a gravitational force equation is increased by a factor of 10, how does this affect the force?
What is the overall effect on displacement if the velocity is increased by a factor of 4 and time is halved?
What is the overall effect on displacement if the velocity is increased by a factor of 4 and time is halved?
What is the change in the gravitational field strength if the mass is doubled and the radius is tripled?
What is the change in the gravitational field strength if the mass is doubled and the radius is tripled?
If a variable x doubles, how does the inversely proportional variable y change?
If a variable x doubles, how does the inversely proportional variable y change?
In a situation where x decreases by a factor of 3, how does y change if y is inversely proportional to the square of x?
In a situation where x decreases by a factor of 3, how does y change if y is inversely proportional to the square of x?
What will be the effect on y if x increases and y is inversely proportional to x squared?
What will be the effect on y if x increases and y is inversely proportional to x squared?
If the velocity is reduced by half, what will happen to the kinetic energy of an object?
If the velocity is reduced by half, what will happen to the kinetic energy of an object?
Flashcards
Relationship (Physics)
Relationship (Physics)
A relationship in physics that describes how a change to one variable affects another.
Directly Proportional
Directly Proportional
A relationship where two variables change in the same direction. If one variable increases, the other increases, and vice versa.
Inversely Proportional
Inversely Proportional
A relationship where two variables change in opposite directions. If one variable increases, the other decreases, and vice versa.
∝ (Proportionality Symbol)
∝ (Proportionality Symbol)
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Constant of Proportionality (k)
Constant of Proportionality (k)
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Direct Square (Quadratic) Relationship
Direct Square (Quadratic) Relationship
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Force of Friction and Normal Force
Force of Friction and Normal Force
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Acceleration and Mass
Acceleration and Mass
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Direct Square Proportionality
Direct Square Proportionality
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Inverse Square Proportionality
Inverse Square Proportionality
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Combined Effect of Multiple Variables
Combined Effect of Multiple Variables
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Kinetic Energy and Velocity
Kinetic Energy and Velocity
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Gravitational Force and Distance
Gravitational Force and Distance
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Displacement, Velocity, and Time
Displacement, Velocity, and Time
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Gravitational Field Strength, Mass, and Distance
Gravitational Field Strength, Mass, and Distance
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Displacement with Uniform Motion
Displacement with Uniform Motion
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Study Notes
Relationships Between Variables
- Physics relationships describe how changes in one variable affect another.
- Two main types exist: direct and inverse.
Direct Relationships
- Direct relationships occur when variables change in the same direction.
- If one variable increases, the other also increases.
- Represented by proportionalities (∝) and expressed as equations like y = kx, where k is a constant.
- If y is directly proportional to x, increasing x by a factor will increase y by the same factor.
- Example: Force of friction is directly proportional to the normal force (Ffriction ∝ Fnormal).
Inverse Relationships
- Inverse relationships exist when variables change in opposite directions.
- If one variable increases, the other decreases.
- Represented as y ∝ 1/x, meaning y is proportional to one over x.
- Inverse relationships can be expressed as equations like y = k/x.
- Example: Acceleration is inversely proportional to mass (a ∝ 1/m).
Direct Square Relationships
- A direct square relationship occurs when a variable is proportional to the square of another.
- Represented as y ∝ x2
- Example: Kinetic energy is directly proportional to the square of velocity (Ek ∝ v2).
Inverse Square Relationships
- In an inverse square relationship, a variable is inversely proportional to the square of another.
- Represented as y ∝ 1/x2 which is expressed as y = k/x2 where k is the constant.
- Example: Gravitational force is inversely proportional to the square of the separation distance (FG ∝ 1/r2)
Multiple Variable Relationships
- Relationships can involve multiple variables.
- Each variable can be analyzed independently, then combined to determine the overall effect.
- Example: Displacement in uniform motion considers velocity and time. If velocity is multiplied by a factor of 4 but time is halved, the displacement effectively doubles.
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