How far does each can slide on the table?

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The discussion focuses on calculating how far paint cans slide on a table after descending a ramp. Each can weighs 46N and slides down a 24-degree ramp at a constant speed of 3.4 m/s. The gravitational force component acting along the ramp is approximately 18.7N, while the kinetic energy equation indicates that the distance slid on the table is about 1.5 meters. The key point is that the cans must have an initial speed to maintain constant velocity, implying that the friction force equals the gravitational force component down the incline. Overall, the analysis emphasizes the equilibrium of forces acting on the cans during their motion.
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Homework Statement


In a hardware store, paint cans, which weigh 46N each, are trasnported from storage to the back of the paint department by placing them on a 24 degree ramp. The cans slide down the ramp at a constant speed of 3.4 m/s onto a table made of the same material as the ramp. How far does each can slide on the table?


Homework Equations


mgsin(x) = component of gravity in the same dimension as the incline on which the object sits
KE = mv²/2
ΔKE = Fd


The Attempt at a Solution


46sin(24) ≈ 18.7
-(46/9.8)(3.4)²/2 = -18.7d
d ≈ 1.5
My problem is if the friction force were equivalent to the force of gravity down the incline, the the paint cans would never move.
 
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The frictional force and the force propelling the cans down the incline must be equal, as the cans are moving at a constantly velocity, so all forces are in equilibrium.

I think we're assuming the cans are originally given some speed to begin with, and aren't placed on the ramp stationary, as the question does say it has a velocity.
 
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