When the National Museum of African American History and Culture was conceived in 2003, Barack Obama was a state senator in Illinois; the acquittal of George Zimmerman in the death of Trayvon Martin was years in the future; and Bill Cosby was a symbol of family decency.

Now, as the museum prepares to open here in September, the nation’s first black president is nearing the end of his second term, Mr. Cosby is accused of being a sexual predator and Americans are engaged in the most charged conversation about race in decades.

As events have complicated the museum’s original mission to be a “healing place,” curators have rushed to catch up with history — documenting the rallies in Baltimore after the death of Freddie Gray — while wrestling with how to tell it. How far to go in depicting the cruelty of slavery and the pain of segregation? How to tell the awful story of Emmett Till? And where does this story end — with the accomplishments of President Obama or with scenes of unrest and violence?

“What’s included, what’s not included, that’s a really, really huge responsibility,” said Kellie Carter Jackson, a scholar of 19th-century African-American history at Hunter College. “It’s probably one of the most difficult tasks in curatorial history.”