How far does each can slide on the table?

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SUMMARY

The discussion focuses on calculating the distance that paint cans slide on a table after descending a 24-degree ramp at a constant speed of 3.4 m/s. The weight of each can is 46N, and the gravitational force component along the ramp is calculated using the equation 46sin(24) ≈ 18.7N. The kinetic energy equation KE = mv²/2 is applied to find the distance on the table, resulting in d ≈ 1.5 meters. The analysis confirms that the frictional force equals the gravitational force component, maintaining equilibrium as the cans slide.

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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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