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 force of gravity varies directly with mass: F = k "." m .
The constant of variation is given as k = 32.2 .
Substitute the value of k into the equation: F = 32.2 m .
The equation representing the force on an object due to gravity is F = 32.2 m .
Explanation
Understanding Direct Variation We are given 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 . We can express this relationship as: F = k "." m where k is the constant of proportionality.
Identifying the Constant of Variation We are also given that the constant of variation due to gravity is 32.2 feet per second squared. This means that k = 32.2 .
Substituting the Constant Now, we substitute the value of k into the equation F = k "." m :
F = 32.2 m
Final Equation Therefore, 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 instance, the elongation of a spring is directly proportional to the force applied to it (Hooke's Law). Similarly, in economics, the total cost of buying multiple items of the same kind is directly proportional to the number of items purchased. Recognizing and applying direct variation helps in predicting outcomes and understanding relationships between quantities in various real-world scenarios.
The force of gravity on an object varies directly with its mass, described by the equation F = 32.2 m . This indicates that for every unit of mass, the force due to gravity increases by 32.2. Therefore, the correct answer is option C: F = 32.2 m .
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