Jung SuWon  is both mental and physical. Here Dr. Kim talks about the physical form of Jung SuWon.
…this art form also has a physical system, and learning the physical form of Jung SuWon is a practical and tangible way to put the spiritual principles of Jung SuWon into practice and to bring you into contact with your Silent Master Consciousness. Your mind and body are one. Therefore, when you practice the Jung SuWon physical form along with the seven mental and spiritual principles, you develop your whole being, not your mind only, not your body only.
Even if you are not enrolled in formal Jung SuWon training you can benefit  and can still apply the principles in your physical life.

Here is the key:  Physical Training Is Overcoming Limitation
Certainly, increased physical strength and the knowledge of self-defense are desirable rewards of Jung SuWon martial art training; they reduce fear and weakness and build true confidence and self-esteem. Tae Kwon Do, Shotokan Karate, and Kung Fu are all similar in the origins of their basic forms. But the quality of physical training in Jung SuWon depends directly on the extent to which the SPIRITUAL training is applied. Learning the martial art moves and forms, learning how to spar effectively with an opponent, and demonstrating ex¬traordinary physical feats (breaking bricks with your bare hand) require that you use all the principles of awareness, balance, visualization, commitment—all the rules of mental conduct—as well as the seven principles of inner power.
Training in the physical form of Jung SuWon requires that you focus all these ideas within the parameters of this structured art form and that you develop yourself and measure your progress in a disciplined manner. Your training, then, can be a feedback system, letting you know where you stand in taking control of your mind and body.