How far will a box slide with a given push and coefficient of kinetic friction?

[psycovic23]

"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 .20 and the push imparts an initial speed of 4.0m/s?"

I'm really stuck as to how to figure out the acceleration...

 

[dextercioby]

"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 .20 and the push imparts an initial speed of 4.0m/s?"

I'm really stuck as to how to figure out the acceleration...

The acceleration is easy to find.It's the acceleration due to kinetic friction.Use the definition for the kinetic friction force and find the acceleration.
UUse the 2 formulas:
$$v(t)=v_{0} +at$$
$$x(t)=x_{0}+v_{0}t+\frac{at^{2}}{2}$$
Chose $x_{0}=0$.

Daniel.

 

[psycovic23]

I'm still kind of stuck..how are you suppose to incorporate acceleration through those equations into f=ma?

Alright, here's what I have so far.

$$x = v_0 ((v-v_0)/a) + a*((v-v_0)/a)^2$$

How do I get the friction into that? And how do I make that equation look neater with the $$tag?$$

 

[dextercioby]

I'm still kind of stuck..how are you suppose to incorporate acceleration through those equations into f=ma?

It's actually the other way around.U use F=ma to find the acceleration and then plug the acceleration in the first (kinetic) equation and find time.Plug time,acceleration and initial velocity in the second (kinematic) equation to find the distance on which the body moves and solve your problem.

Daniel.

PS.The F=ma is to be applied for the kinetic fricton force,bu first u have to know its definition.I assume u do.

 

[psycovic23]

But if you don't know the initial push, how can you set up F=ma?

What I thought was:

$$F_p - u_k mg = ma$$

 

[dextercioby]

But if you don't know the initial push, how can you set up F=ma?

What I thought was:

$$F_p - u_k mg = ma$$

No,no,no,the word 'push' just stands for an explanation to why your body has initial velocity.In your equation it shouldn't stand and therefore the force shoud be equaled to 0.
Puttin' 0 in your equation above,it gives you the acceleration due to friction which is uded to determine the length.

Daniel.

PS.It should have been given the time in which that initial velocity is acquired.Only then u could have been able to compute the "push".

 

[psycovic23]

Ah, I understand now! Thank you very much! The whole F_p thing was really throwing me off.