The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents [tex]$F$[/tex], the force on an object due to gravity according to [tex]$m$[/tex], the object's mass?
A. [tex]$F=16.1 m$[/tex]
B. [tex]$F=\frac{16.1}{m^2}$[/tex]
C. [tex]$F=32.2 m$[/tex]
D. [tex]$F=\frac{32.2}{m^2}$[/tex]
Answer (2)
The problem states that force varies directly with mass.
The constant of variation is 32.2.
Substitute the constant into the direct variation equation.
The equation representing the force is F = 32.2 m .
Explanation
Understanding the Problem The problem states that the force of gravity on an object varies directly with its mass. This means that the force F is proportional to the mass m . The constant of proportionality is given as 32.2 feet per second squared. We need to find the equation that represents this relationship.
Setting up the Equation Since the force F varies directly with the mass m , we can write the relationship as: F = k "." m where k is the constant of variation.
Identifying the Constant of Variation We are given that the constant of variation is 32.2 feet per second squared. Therefore, k = 32.2 .
Substituting the Value of k Substitute the value of k into the equation F = k "." m :
F = 32.2 m
Final Answer The equation that represents the force on an object due to gravity according to its mass is F = 32.2 m .
Examples
Understanding direct variation is crucial in physics. For example, the equation F = 32.2 m shows how the gravitational force on an object changes with its mass. In real life, this concept is used to calculate the weight of objects, design structures that can withstand gravitational forces, and understand the motion of objects under gravity. Knowing how force and mass relate helps engineers and scientists make accurate predictions and build safe and efficient systems.
The force of gravity on an object varies directly with its mass, represented by the equation F = 32.2 m . The correct option from the choices given is C. This equation shows how gravitational force increases proportionally with mass.
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