Proportionality statements in physics

In summary, the conversation discusses the process of deriving a linear equation using given data points for the values of Fc and F. The proportionality statement of Fc being proportional to 4√F allows for a linear graph, with a slope of 3/0.02. However, this slope may be underestimated for the given data points and adding a y-intercept to the equation may be necessary. The suggested linear equation is Fc = 177√[4]{F} - 165.
  • #1
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Homework Statement


A chart has values of Fc (dependant): 10, 15, 20, 25, 30, respectively. The independant variable, F, has values 0.98, 1.07, 1.16, 1.32, 1.50, respectively. These values form a root graph.

Fc is proportional to 4√F, this is the proportionality statement allowing me to make the graph linear. The slope of the linear is 3 / 0.02.

How can I derive an equation for the linear using the slope and values I have if the slope is the constant?

Homework Equations

The Attempt at a Solution


my attempt is[/B]
4√F × constant (slope)
however it does not work
 
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  • #2
Have you considered adding y-intercept to your equation? I plotted your data and obtained the linear equation [itex] F_c = 177\sqrt[4]{F}-165 [/itex]. Also, I think the slope you have (3/0.02) is too underestimated for your data points.
 

Related to Proportionality statements in physics

What are proportionality statements in physics?

Proportionality statements in physics are mathematical expressions that describe the relationship between two or more variables. They show how one variable changes in proportion to another, and can help us understand the behavior and properties of physical systems.

How are proportionality statements used in physics?

Proportionality statements are used in physics to express the quantitative relationships between physical quantities. They are often used to make predictions, analyze data, and develop mathematical models for physical phenomena.

What is the difference between direct and inverse proportionality?

In direct proportionality, two variables change in the same direction, meaning that an increase in one variable results in a proportional increase in the other. In inverse proportionality, two variables change in opposite directions, meaning that an increase in one variable results in a proportional decrease in the other.

How do you represent proportionality statements mathematically?

Proportionality statements can be represented using the symbol ∝ (proportional to). For example, if we say that x is proportional to y, we can write this as x ∝ y. In addition, we can use the proportionality constant k to represent the specific numerical relationship between the variables, such as x = ky.

What are some real-life examples of proportionality statements in physics?

Proportionality statements can be found in many areas of physics, such as Newton's Law of Universal Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Other examples include Ohm's Law, which relates the voltage, current, and resistance in an electrical circuit, and Boyle's Law, which describes the relationship between pressure and volume in a gas at a constant temperature.

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