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?
[tex]$F=16.1 m$[/tex]
[tex]$F=\frac{16.1}{m^2}$[/tex]
[tex]$F=32.2 m$[/tex]
[tex]$F=\frac{32.2}{m^2}$[/tex]
Answer (2)
The force of gravity varies directly with mass, so F = k × m .
The constant of variation is 32.2.
Substitute the constant 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 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 variation 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.
Substituting the Constant of Variation We are given that the constant of variation is 32.2 feet per second squared, so k = 32.2 . Substituting this value into the equation, we get: F = 32.2 m
Final Equation Therefore, the equation that represents the force F on an object due to gravity as a function of its mass m is F = 32.2 m .
Examples
Understanding direct variation is crucial in physics. For example, the weight of an object on Earth varies directly with its mass. If you know the mass of an object, you can calculate its weight using the equation W = m g , where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s 2 or 32.2 ft/s 2 ). This principle is used in various applications, such as designing structures, calculating the force needed to move objects, and understanding the motion of celestial bodies.
The equation that represents the force on an object due to gravity in terms of its mass is F = 32.2 m . This is derived from the direct variation relationship between force and mass, where 32.2 is the constant of variation. Therefore, the correct choice from the options provided is F = 32.2 m .
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