Final answer:
The magnitude of the force F applied to the 7 kg block, taking into account Newton's Third Law of Motion and Newton's second law for both blocks, is determined to be 18 N.
Step-by-step explanation:
To find the magnitude of the force F applied to the 7 kg block, we first need to consider Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.
Given that the 7 kg block exerts a force of 4 N on the 3 kg block, the 3 kg block must exert an equal and opposite force of 4 N on the 7 kg block. The 3 kg block also has an additional 2 N force acting on it.
Since the surface is frictionless, the only horizontal forces acting on the 3 kg block are the 4 N force from the 7 kg block and the 2 N external force. These forces add up to give the 3 kg block a total force of 6 N. To find the acceleration (a) of the 3 kg block, we use Newton's second law (F = ma):
F = ma
6 N = 3 kg * a
a = 6 N / 3 kg
a = 2 m/s²
Because the blocks are initially in contact, they will have the same acceleration. Now, applying Newton's second law to the 7 kg block:
F - 4 N = 7 kg * 2 m/s²
F - 4 N = 14 N
F = 14 N + 4 N
F = 18 N
Therefore, the magnitude of the force F applied to the 7 kg block is 18 N.