Question

Use the simulation to answer the question.

Answer 1

Answer:

The gravitational force varies directly with mass of the objects and

inversely with the square of the distance between them, therefore,

doubling the mass doubles the gravitational force while halving the

distance between the masses quadruples the gravitational force. The

option that crate the greatest increase in the gravitational force is halving

the distance between the masses.

Step-by-step explanation:

Answer 2

The gravitational force varies directly with mass of the objects and

inversely with the square of the distance between them, therefore,

doubling the mass doubles the gravitational force while halving the

distance between the masses quadruples the gravitational force. The

option that create the greatest increase in the gravitational force is;

Halving the distance between the masses.

Reasons:

The known parameters are;

m₁ = 200 kg

m₂ = 400 kg

The distance between the centers of the masses = 8 meters

Required:

Change in variable that produces the greatest increase in the gravitational

force.

Solution;

The equation for the gravitational force is $F = \mathbf{G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}}$

The gravitational force between the masses is therefore;

$F =6.67408 \times 10^{-11} \times \dfrac{200 \times 400}{8^{2}} = 8.3426 \times 10^{-8}$

F = 8.3426 × 10⁻⁸ N

Doubling the mass of m₂ gives;

$F_{2 \cdot m } = G \cdot \dfrac{m_{1} \cdot 2 \times m_{2}}{r^{2}} = \mathbf{2 \times G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}}$

Doubling the mass of m₂, doubles the gravitational force.

$F_{2 \cdot m }$ = 2 × F = 2 × 8.3426 × 10⁻⁸ N = 1.66852 × 10⁻⁷ N

Halving the distance between the masses gives;

$F_{\frac{r}{2} } =G \cdot \dfrac{m_{1} \cdot m_{2}}{\left(\dfrac{r}{2} \right) ^{2}} = 4 \times G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}$

$F_{\frac{r}{2} }$ = 4 × F = 4 × 8.3426 × 10⁻⁸ N = 3.33704 × 10⁻⁷ N

Therefore, halving the distance between the masses quadruples (multiplies

by 4) the gravitational force between the masses.

Halving the distance between the masses creates the greatest

increase in the gravitational force because the gravitational force varies

with inverse of the square of the distance between the masses, and,

halving the distance between the masses has the effect of quadrupling the

gravitational force.

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