Question

the force of gravity on an object varies directly with its mass. the constant of variation due to gravity is second squared. which equation represents f, the force on an object due to gravity according to m, the mass?

f = 16.1m

f = \frac{16.1}{m^{2}}

f = 32.2m

f = \frac{32.2}{m^{2}}

Explanation:

Step1: Recall the direct - variation formula

The formula for direct variation is \(y = kx\), where \(k\) is the constant of variation. In the context of force \(F\) and mass \(m\) (since \(F\) varies directly with \(m\)), the formula is \(F=km\).

Step2: Identify the value of the constant of variation

The constant of variation due to gravity (in the English system of units, where weight (force) is measured in pounds and mass is measured in slugs) is \(k = 32.2\) (pounds per slug).

Answer:

C. \(F = 32.2m\)