How were class tensions affected by the Industrial Revolution?
They took a different form
The industrial revolution meant the aristocracy lost the leadership of the economy as the Bourgeoisie rose tremendously in power. The Working Class emeged as well since farmers moved from the countryside to find jobs in factories in the cities. Tensions were no longer between the Bourgeoisie and the aristocracy or between the people and the aristocarcy(the class of landlords), they were fueled by the opposition between the working class(what Marx called the Proletariat) and the Bourgeoisie(the class of factory owners).
In the US, the opposition concerned the issue of slavery and tariffs before the Civil War, the North had an economy based on manufacturing whereas the South had an economy which relied on agriculture and free trade with Europe. The North longed for tariffs to protect its industry from European competition and the culmination was the Civil War and the passing of the Morill tariffs.
After the Civil War, Industry triumphed and this is how tensions between the Working Class and the Bourgeoisie rose. Cities such as Philadelphia or Chicago knew episodes of strikes. Labor Unions such as the Knights of Labor, the AFL or even the Wobblies( the Industrial Workers of the World whose members were mostly poor unskilled European born workers) emerged during what is remembered as the Gilded Age. The expression was coined by Mark Twain in his eponymous novel and meant prosperity was only on the surface and did not affect lower classes.