# Kinetic and Static friction

1. Oct 22, 2008

### fishingspree2

1. The problem statement, all variables and given/known data
A 2.5 kg box in on a 53 degrees inclined plane. mu-kinetic = 0.25 and mu-static=0.5. Find it's acceleration if it is initially standing still.

2. Relevant equations
F = ma

3. The attempt at a solution
The X component of the gravity is = 2.5*g*sin(53)
Normal force = 2.5*g*cos(53)
Maximum static force = mu-static*N = 0.5*2.5*g*cos(53)
To my understanding, since it is not moving, I will use mu-static because once the force becomes greater than maxmum static force by an infinitely small number, it is accelerating close to the accelerating value found using maximum static force.
http://img252.imageshack.us/img252/8263/frictionto4.jpg [Broken]

F = ma
[2.5*g*sin(53)] - [0.5*2.5*g*cos(53)] = 2.5*a
g [sin(53) - 0.5*cos(53)] = a
a= 4.87 m/s^2

however, by looking in the answer booklet, this is in correct, and the acceleration is found by using mu-kinetic
g [sin(53) - 0.25*cos(53)] = a
a= 6.35 m/s^2

it really makes more sense in my head using mu-static instead of mu-kinetic
can somebody show me why it is wrong?

Last edited by a moderator: May 3, 2017
2. Oct 22, 2008

### PhanthomJay

If the box is accelerating from an initially at rest position, then it must be moving. You can't use static friction forces for objects in motion. The box is initially standing still either because you are holding it there, or because it has come to a momentary stop after someone shoved it up the incline.