Sweep = to clean especially a floor by using a brush to collect the dirt into one place from which it can be removed.

Sweep along = to make somebody very interested or involved in something, especially in a way that makes them forget everything else.

“Time is the substance I am made of. Time is a river which sweeps me along, but I am the river; it is a tiger which destroys me, but I am the tiger; it is a fire which consumes me, but I am the fire.”
–Jorge Luis Borges

Art – Henri Julien Rousseau‘s tiger.