The Internet of Things (IoT) is becoming ubiquitous in our daily life. IoT networks that are made up of devices low power, low memory, and low computing capability appears in many applications such as healthcare, home, agriculture. IPv6 Routing Protocol for Low Power and Lossy Network (RPL) has become a standardized routing protocol for such low-power and lossy networks in IoT. RPL establishes the best routes between devices according to the requirements of the application, which is achieved by the Objective Function (OF). Even though some security mechanisms are defined for external attackers in its RFC, RPL is vulnerable to attacks coming from inside. Moreover, the same attacks could has different impacts on networks with different OFs. Therefore, an analysis of such attacks becomes important in order to develop suitable security solutions for RPL. This study analyze RPL-specific attacks on networks using RPL's default OFs, namely Objective Function Zero (OF0) and the Minimum Rank with Hysteresis Objective Function (MRHOF). Moreover, mobile attackers could affect more nodes in a network due to their mobility. While the security solutions proposed in the literature assume that the network is static, this study takes into account mobile attackers.