Question

1. draw a graph that represents how gravitational force changes when distance increases. distance will be on the x axis and force on the y.

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force \(F = \frac{Gm_1m_2}{r^2}\), where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between them.

Step2: Analyze the relationship between force and distance

From the formula \(F=\frac{k}{r^2}\) (where \(k = Gm_1m_2\) is a constant for a given pair of masses), we can see that as \(r\) (distance) increases, \(F\) (gravitational force) decreases. The relationship is an inverse - square relationship.

When \(r = 1\), \(F=k\); when \(r = 2\), \(F=\frac{k}{4}\); when \(r = 3\), \(F=\frac{k}{9}\) etc.

Answer:

The graph will be a curve that starts at a relatively high value on the \(y\) - axis (when \(x = 0\), \(F\) is undefined in the physical sense, but for non - zero small \(x\) values, \(F\) is large) and decreases rapidly as \(x\) (distance) increases. It will approach the \(x\) - axis (but never touch it) as \(x\to\infty\). The general shape is similar to the right - hand side of a hyperbola \(y=\frac{k}{x^2}\) in the first quadrant.