Questions: 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 F, the force on an object due to gravity according to m, the object's mass? F=16.1 m F=16.1/m^2 F=32.2 m F=32.2/m^2

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 F, the force on an object due to gravity according to m, the object's mass?
F=16.1 m
F=16.1/m^2
F=32.2 m
F=32.2/m^2

Transcript text: 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 $F$, the force on an object due to gravity according to $m$, the object's mass? $F=16.1 m$ $F=\frac{16.1}{m^{2}}$ $F=32.2 m$ $F=\frac{32.2}{m^{2}}$

Solution

Solution Steps

Step 1: Understand the Relationship

The problem states that the force of gravity on an object varies directly with its mass. This means that the force $ F $ is directly proportional to the mass $ m $.

Step 2: Identify the Constant of Variation

The constant of variation due to gravity is given as 32.2 feet per second squared. This constant is used in the equation that relates force and mass.

Step 3: Formulate the Equation

Since the force $ F $ varies directly with mass $ m $, the equation can be written as: \[ F = k \cdot m \] where $ k $ is the constant of variation. Given $ k = 32.2 $, the equation becomes: \[ F = 32.2m \]

Step 4: Select the Correct Equation

Among the given options, the equation that represents the force on an object due to gravity according to its mass is: \[ F = 32.2m \]