The Routing Protocol for Low-Power and Lossy Networks (RPL) is the routing protocol standardized for constrained environments such as 6LoWPAN networks, and is considered as the routing protocol of the Internet of Things (IoT). However, this protocol is subject to several attacks that have been analyzed on static case. Nevertheless, IoT will likely present dynamic and mobile applications. In this paper, we introduce potential security threats on RPL, in particular Sybil attacks when the Sybil nodes are mobile. In addition, we present an analysis and a discussion on how network performances can be affected. Our analysis shows, under Sybil attacks while nodes are mobile, that the performances of RPL are highly affected compared to the static case. In fact, we notice a decrease in the rate of packet delivery, and an increase in control messages overhead. As a result, energy consumption at constrained nodes increases. Our proposed attacks demonstrate that Sybil mobile nodes can easily disrupt RPL and overload the network with fake messages making it unavailable. Based on the obtained results we provide some recommendations to tackle this issue.