Is it permissible to sit or lean on a car on Shabbat?
A car, of course, is considered Muktzeh on Shabbat, and hence, like with all Muktzeh objects, one may not move a car on Shabbat. When one sits or leans on a car, the car remains stationary but is shaken and jostled. Would sitting or leaning on a car thus constitute "moving" a Muktzeh item and be forbidden on Shabbat?
The authorities advance a number of arguments to allow sitting or leaning on a car on Shabbat. Firstly, Halacha considers a human corpse Muktzeh, but nevertheless permits washing and smearing oil on a corpse on Shabbat. Even though the body is slightly jostled during the process of washing and smearing, this does not constitute "moving" a Muktzeh item because the body remains stationary. Similarly, even though a car shakes a bit when a person leans or sits on it, this does not qualify as "moving" with respect to the laws of Muktzeh.
Furthermore, many authorities, including the Be'er Moshe (work of responsa by Rabbi Moshe Stern of Debereczyn), classify cars under the category of Keli She'melachto Le'issur – utensils whose primary function entails a forbidden activity on Shabbat. Halacha permits moving a Keli She'melachto Le'issur on Shabbat to use it in a permissible fashion. For example, one may use a pen – an instrument used primarily for writing – to scratch his back on Shabbat. Likewise, one may move a car to use it for a permissible purpose, and hence it is permissible to sit or lean on the car even if it causes the car to "move."
Thirdly, the Rambam explained the prohibition of Muktzeh as a safeguard against carrying in a public domain on Shabbat. The Sages forbade handling certain items even indoors so as to prevent against the possibility of people forgetfully carrying these items into the public domain. Of course, this concern does not arise with regard to a car; nobody is going to forgetfully carry the car through a public domain. Thus, since the reason underlying the Muktzeh prohibition does not apply to car, it is not subject to this prohibition and it may be moved on Shabbat.
Indeed, Chacham Ovadia Yosef ruled that it is permissible to sit or lean on a car on Shabbat, despite the fact that the car will be jostled and shaken as a result.
