Kinetic and Static friction

[fishingspree2]

Homework Statement

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.

Homework Equations

F = ma

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

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?

 

[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.

 

[baba89]

Your solution using mu-static is incorrect because static friction is the force that opposes the motion of an object when it is at rest. In this case, the box is initially at rest, so the static friction force will be equal to the applied force (the component of gravity pulling the box down the incline). Therefore, the maximum static force will not be used in the equation because it is not being reached - the box is not moving.

To find the acceleration, we must use the equation F = ma, where F is the net force acting on the box. In this case, the net force is the component of gravity pulling the box down the incline minus the kinetic friction force (since the box is not moving). Therefore, the correct equation to use is:

F = mgsin(53) - mu-kinetic*mgcos(53) = ma

Solving for a, we get a = g(sin(53) - mu-kinetic*cos(53)) = 6.35 m/s^2.

This is the correct answer because we are looking for the acceleration of the box when it is moving, which is why we use the kinetic friction coefficient. The maximum static force is only relevant when the box is at rest and about to start moving, but in this case, the box is already moving.

I hope this explanation helps clarify the concept of kinetic and static friction for you. Remember, kinetic friction is the force that opposes the motion of an object that is already moving, while static friction is the force that opposes the motion of an object that is at rest. Keep up the good work in your studies!