Final answer:
The force with which one half of the rod acts on the other during motion after an impulse cannot be determined without additional information on the motion post-impulse or the time during which the impulse acts. Concepts of internal forces, impulse, and Newton's Third Law are involved in the analysis.
Step-by-step explanation:
A uniform rod of mass m=5 kg and length l=90cm is struck with an impulse resulting in a momentum of p = 3 Ns. To find the force with which one half of the rod acts on the other during motion, we can apply the concepts of impulse and Newton's laws of motion.
When the rod is struck, the entire rod acquires a linear momentum of 3 Ns. Since the impulse is applied on one end, there is a tendency for the rod to rotate as well. According to Newton's Third Law, the internal forces between the two halves of the rod must be equal and opposite. These internal forces must also account for the movement of the rod such that the center of mass of the rod moves at a velocity which gives it the linear momentum of 3 Ns.
To determine the internal force, we would need to consider the properties of a rotating rigid body and possibly the conservation of angular momentum. However, without additional information regarding the specifics of the motion post-impulse, such as angular velocity or the time during which the impulse acts, we cannot specify the exact force with which one half of the rod will act on the other half. In practice, this would involve a detailed analysis including angular momentum, torque, and the distribution of mass within the rod.