The pushed box with kinetic friction and an inital speed

[NastyAccident]

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.

 

[einstein_a_go_go]

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

 

[baba89]

Based on the given information, we can use the equations of motion to calculate the distance the box will travel. First, we need to find the acceleration of the box, which can be determined by using the equation EFx/m = ax. We know that the only force acting on the box in the horizontal direction is the force of friction, so we can rewrite the equation as (Fa - uk*Fn)/m = ax. We also know that Fn = mg, so the equation becomes (Fa - uk*m*g)/m = ax. Now, we need to find the force of friction, Fa, which can be calculated using the equation Fa = uk*Fn = uk*mg. Plugging this into our previous equation, we get (uk*mg - uk*m*g)/m = ax. Simplifying, we get (uk*g) = ax.

Next, we can use the equation V^2 = Vo^2 - 2a(delta x) to calculate the distance the box will travel. We know that Vo = 3.7 m/s and Vx = 0, so the equation becomes (3.7)^2 = 0^2 - 2(uk*g)(delta x). Solving for delta x, we get delta x = (3.7)^2 / (2*uk*g). Plugging in the given value for uk (0.25) and the acceleration due to gravity (9.8 m/s^2), we get delta x = 2.72 m. Therefore, the box will travel 2.72 meters before coming to a stop due to the force of friction.

It's important to note that Fa and m in this problem represent the force of friction and the mass of the box, respectively. These values were not given in the problem, so you would need to make some assumptions or find additional information to solve for them. It's also important to consider the units of the given values and make sure they are consistent in your calculations.