Applying Newton's Second Law

Newton's Second Law of Motion states that the net force acting on an object is equal to the product of its mass and acceleration (\(F=ma\)). We apply this fundamental principle to determine the forces \(F_1\) and \(F_2\).

Calculating Force \(F_1\)

Object A has a mass \(m_A = 4\text{ kg}\) and is accelerated at \(a_A = 7\text{ m/s}^2\). The force \(F_1\) required is:

\(F_1 = m_A \times a_A\)

\(F_1 = 4\text{ kg} \times 7\text{ m/s}^2\)

\(F_1 = 28\text{ N}\)

Calculating Force \(F_2\)

Object B has a mass \(m_B = 6\text{ kg}\) and is accelerated at \(a_B = 4\text{ m/s}^2\). The force \(F_2\) required is:

\(F_2 = m_B \times a_B\)

\(F_2 = 6\text{ kg} \times 4\text{ m/s}^2\)

\(F_2 = 24\text{ N}\)

Comparing the Forces

We now compare the magnitudes of the two forces:

\(F_1 = 28\text{ N}\)

\(F_2 = 24\text{ N}\)

Since \(28\text{ N}\) is greater than \(24\text{ N}\), the relationship is \(F_1 > F_2\).

Conclusion

The calculation shows that \(F_1\) is greater than \(F_2\). Therefore, the relationship \(F_1 > F_2\) only holds true.