# Solving for distance using only initial velocity and coefficient of friction

1. Nov 24, 2008

### manuela4

This problem is quite difficult for me. I know that there's a way to do this, but i can't figure it out. Could someone point me in the right direction? i dont need a solution, but a process would be nice.

1. The problem statement, all variables and given/known data
A box is given an initial push so that it slides across the floor. How far will it go, given that the coefficient of friction is 0.30 and the push imparts an initial speed of 3.0 m/s?

so Vi = 3.0 m/s, Vf= 0 m/s and Mu = .3
gravity is always active (at 9.81 m/s2), but i have no mass to calculate its force.
2. Relevant equations
all i know for friction:
F=ma (but i dont have mass, acceleration)
F= Mu Fn (Mu being the coefficient of friction, Fn being normal force)
i havnt chosen a distance equation because i dont have enough variables to do so.

3. The attempt at a solution
Without a formula, i cant solve... i cant even get started.

2. Nov 24, 2008

### mgb_phys

Use conservation of energy. You start with kinetic energy it goes into friction (ie heat).
Energy is force * distance, where the force is the frictional force slowing it down.

3. Nov 24, 2008

### wisemo

You sure the question states only that? Cause I strongly think that there's not enough data to solve this problem.

4. Nov 24, 2008

### mgb_phys

The mass cancels.
KE = 1/2 mv^2
Friction = distance*mgu

5. Nov 26, 2008

### wisemo

mgb's prefectly right. apologies for not recognising that :)

6. Mar 28, 2010

### gilliganfrog

Actually, althought relating the Kinetic Energy equation to the equation about friction and distance might be conceptually valid, it isn't the clue this person needed.

At the early point (probably around chapter 4) of an "elementary physics" textbook, a student encounters problems where, given an initial velocity and coefficient of friction , the student is expected to provide the resulting final displacement. This is a stage of the textbook where kinetic energy equations and "work" equations have not yet been introduced, therefore there is a different solution.

Since this person made their inquiry in November of 2008, I'm sure they're not waiting for the answer anymore, but I will return with an answer tomorrow.

7. Feb 24, 2011

### huntr83

I have the same problem, except that initial velocity is 2m/s
I know this is a bump, but it is the closest I can get to my question

8. Feb 23, 2012

### mcloudsound

I have a similar question yet in reverse.

Given:
Final displacement = 12m
Coefficient of Friction = .28

Find:
Initial velocity = 0

I am assuming to look for an equation that cancels masses out, yet need help with the next step

9. Feb 23, 2012

### mcloudsound

NVM I found a working formula.

1/2mv^2=displacement*mgu

so the masses cancel leaving

1/2v^2=Δxgu (horizontal direction)

Thanks for everyone else posting questions!