Observing how humans interact with each other and how they manipulate objects, offer insight on interaction mechanisms and how these are influenced by the physical properties of the used objects. These insights can support a more informed design of robot controllers meant to manipulate objects in collaboration with humans. In this work, we study human-to-human handovers of cups filled with various amount of liquid and textures and investigate to which extent the manipulation strategy depends on: 1) the individual preference; 2) whether the cup is filled with water or not; and 3) the cup physical properties. An analysis of the human giver's hand acceleration, velocity, and position during the handover of different cups under two liquid level conditions, allows to distinguish between careful and not careful (normal) manipulation. We quantify to which extent the liquid level inside the cups influences the carefulness level of human manipulation. Finally, our study reveals that the cups' physical properties, such as fragility, breakability, and deformability, play a role in shaping the carefulness of the manipulation. We apply these findings to human-robot scenarios by developing a robot controller capable of detecting, in realtime, if the human is being more careful than normal, and adapting the robot's approach of interaction accordingly. Additionally, we show that the detection of a careful manipulation, depending on the experimental context, may provide the robot with information concerning the human partner's intention or need for (manipulation) assistance.