Question

3 multiple choice 1 point
two objects attract each other with a force of gravity (f grav) of 324 n. if the distance separating the objects is tripled, then what is the new force of gravitational attraction?
3n
120n
9n
36n

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force is \(F_{grav}=G\frac{m_1m_2}{r^{2}}\), 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. Let the initial force \(F_{1}=G\frac{m_1m_2}{r_{1}^{2}} = 324\space N\). When the distance is tripled, \(r_{2} = 3r_{1}\). The new force \(F_{2}=G\frac{m_1m_2}{r_{2}^{2}}\).

Step2: Substitute \(r_{2}=3r_{1}\) into the formula for \(F_{2}\)

Substitute \(r_{2}\) into \(F_{2}\): \(F_{2}=G\frac{m_1m_2}{(3r_{1})^{2}}=G\frac{m_1m_2}{9r_{1}^{2}}\). Since \(F_{1}=G\frac{m_1m_2}{r_{1}^{2}} = 324\space N\), then \(F_{2}=\frac{F_{1}}{9}\).

Step3: Calculate \(F_{2}\)

We know \(F_{1} = 324\space N\), so \(F_{2}=\frac{324}{9}=36\space N\)

Answer:

36 N