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 is \(F = \frac{Gm_1m_2}{r^2}\), 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 \(F=\frac{Gm_1m_2}{r^2}\), we can see that \(F\) is inversely proportional to \(r^2\). As \(r\) (distance) increases, \(F\) (gravitational force) decreases.

Step3: Sketch the graph

When \(r = 1\), \(F=\frac{Gm_1m_2}{1}=Gm_1m_2\). When \(r = 2\), \(F=\frac{Gm_1m_2}{4}\). When \(r = 3\), \(F=\frac{Gm_1m_2}{9}\) and so on. The graph will be a curve that starts at a non - zero value on the \(y\) - axis (when \(r = 0\), the formula is not valid in the context of two separate objects, but as \(r\) approaches a small non - zero value, \(F\) is large) and decreases as \(r\) (on the \(x\) - axis) increases. The general shape is a hyperbola in the first quadrant (since distance \(r>0\) and force \(F>0\) for two real objects).

Answer:

The graph is a curve (a hyperbola in the first quadrant) that shows a decrease in gravitational force as the distance increases.