The pushed box with kinetic friction and an inital speed

AI Thread Summary
A box is pushed with an initial speed of 3.7 m/s across a surface with a coefficient of kinetic friction of 0.25. The discussion revolves around calculating how far the box will slide before coming to a stop, with initial attempts focusing on forces and accelerations. One participant suggests simplifying the problem by using energy considerations, specifically the initial kinetic energy and the work done against friction. The need for clarity on the forces involved and proper application of equations is emphasized, as the original poster struggles with identifying the necessary variables. Ultimately, the solution involves balancing kinetic energy against frictional work to determine the distance traveled.
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Homework Statement


A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.25 and the push imparts an initial speed of 3.7 m/s?

Homework Equations


E is sigma
EFy/m = ay
-> Fn - mg = 0
-> because ay = 0
-> Fn = mg
EFx/m = ax
-> (Fa - uk*Fn)/m = ax
-> (Fa - uk*m*g)/m = ax

V^2 = Vo^2 - 2a(delta x)

The Attempt at a Solution



yo = 0
y = ?
Vox = 3.7 m/s
Vx = 0
t = ?

I manipulated the equation so I could get ax... The end result was...

ax = Fa / m - uk * g

However, I do not know what Fa is nor do I know what m is.. This problem has me stumped and if anybody could direct me to the proper logic or correct my logic I would be really content/happy!

I'm really unsure of how to do this type of problem. We were not given an example in class regarding a problem like this.
 
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hi,

I think you are making the situation too complicated. Problems can usually be solved EITHER by forces and accelerations OR by energy considerations.

I think here you would be better off considering the initial kinetic energy and the work done against friction as the block slides.

Cheers
 
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