To calculate the force needed to hold down a hydrogen-filled balloon, one must first determine the total weight of the balloon and the hydrogen it contains. The buoyancy force of the air acting on the balloon, which is dependent on the volume of hydrogen, must also be considered. It's crucial to remember that force is measured in Newtons while mass is measured in kilograms, as mixing these units can lead to significant errors, especially in academic settings. The discussion highlights the confusion surrounding unit conversions and the importance of using the correct measurements in calculations. Understanding these concepts is essential for accurately solving physics problems related to buoyancy and force.