Calculating the force exerted on a ferromagnetic object by a solenoid's magnetic field is complex due to the field gradient. The gradient is significant because it affects the net force based on the difference in force at each pole of the magnet. Inducing a magnetic dipole in the object adds further complexity to the calculations. For practical applications, such as building a DIY coilgun with 8J of energy, trial-and-error may be necessary to achieve desired results. Understanding these principles is crucial for effective design and experimentation.