The friar motivation to go to the monument is stop romeo from killing himself. The friar knows that the message he sent to romero, romeo did not get it which the friar know that romero would do something stupid like killing himself.
romeo
Because he heared the noises from outside of the tomb.
To break into Capulet's tomb
Balthazar is unable to enter the tomb with the Friar because he is not allowed to accompany him due to religious beliefs or customs, or because the rules of the tomb or site do not permit animals. Additionally, the tomb may be too confined or dangerous for an animal to enter.
Love.
Because he knows Juliet is about to wake up and Romeo will not be there, since Friar John was not able to deliver his message.
Juliet refused to go.
He had to leave, for the "police" was on their way. He had no choice but to go...
Friar Lawrence requests a crowbar to open Juliet's tomb and a letter to write to Romeo explaining the situation with Juliet.
Friar Laurence tells the watchman that he is hurrying to get to the Capulet tomb to prevent Juliet from waking up and discovering that Romeo is dead. He instructs the watchman to go and fetch the prince and bring him to the tomb.
to get Juliet because she is only in a coma, she only looks dead
A letter was sent from Friar Lawrence to Romeo who had been banished. Romeo had not intercepted this letter, and after having knowledge that Juliet was 'dead' he rushed to the tomb.