A late-morning stillness had settled over a November Saturday in a cozy blanket of suburban serenity. Suddenly, at stadium-level blast, there came the shattering rock ’n’ roll roar of victory:

We will, we will rock you

We will, we will rock you

The sounds of something unleashed — banging pots, honking horns, primal shouts — burst from all directions in Maplewood, New Jersey. And as another Queen song boomed from the muscular loudspeakers in his garage, Zack Kurland stood at the edge of his driveway, arms raised like Rocky.

We are the champions

We are the champions

His wife, Neena Kumar, came running and leapt into his arms. News had just arrived that Joseph R. Biden Jr had been declared the winner of the presidential election of 2020, and now the two were twirling in an impromptu public dance of triumph.

The moment evoked an iconic American image: a World War II sailor spontaneously kissing a woman in a nurse’s uniform in Times Square after the news of victory in Europe. Only instead of V-E Day, this was V-B Day: Victory for Biden.

But not everyone was dancing. Triumph in a foreign war unifies a country; triumph in an election has the lurking potential to further divide. And by Sunday morning, some of the celebration and grieving had melted away to expose a difficult question for divided families and a divided nation: Now what?

True, a record number of more than 75 million Americans had voted for Biden, the Democratic challenger, and his running mate, Kamala Harris, the first woman elected as Vice-President. Also true was that more than 71 million others now had to grapple with the concept that their candidate — Donald J. Trump, the Republican incumbent — would most likely be branded by his own worst epithet: loser. By refusing, for now, to publicly accept the election results, Trump was all but inviting dance-interrupting discord. And some accepted his invitation.

Trump supporters held “Stop the Steal” rallies outside state capitols across the country, though their cries of electoral corruption sometimes came as news of Biden’s declared victory was lighting up smartphones everywhere.

In Sacramento, California, videos captured confrontations that devolved into physical assaults; some in the scrum wore the black-and-yellow polo shirts often associated with the Proud Boys, a far-right, pro-Trump group not unfamiliar with violence. Another video, from Salem, Oregon, showed a man in Proud Boys apparel discharging what appeared to be pepper spray, after which a crowd battered a vehicle with fists and a baseball bat.

These small moments reflect the sizable fissure in the collective American psyche that Biden sought to begin closing in his speech on Saturday night. With a stand of American flags behind him, he said the time had come to restore the nation’s soul; to embrace the first three words of the Constitution: “We the people.”

“It’s time to put away the harsh rhetoric,” he said. “To lower the temperature. To see each other again. To listen to each other again.”

His words seemed directed as much to the individual American as to the nation at large, as if to recognise the gaping rifts created over the four tumultuous years since Trump was elected. Friendships have fractured. Workplace relationships have cooled. Family gatherings have been altered by fears that a request to pass the salt might somehow lead to a political brawl.

In Trump-solid Mercer County, Pennsylvania, a retired special education teacher named Beverly Graham, a Democrat, celebrated the big news on Saturday by pouring a glass of honey whiskey. She drank it in quiet toast, then tackled the chore of cleaning the bathrooms.

It has been a hard four years for Graham, with various political disagreements, including with sons who went from supporting Obama to supporting Trump. Especially difficult was the brutal mocking of Democrats — in other words, people like her — on social media by members of her church. Their disdain was so vitriolic that she had trouble attending Sunday services.

“I just don’t think it’s ever going to be the same,” Graham, 65, said. “Because I felt like it was beyond political. It was personal.”

New York Times News Service