Will the Block Move? Understanding Static and Kinetic Friction

[debbers111]

Homework Statement

A block whose weight is 45.0N rests on a horizontal table. A horizontal for of 36.0N is applied to the block. The coefficients of static and kinetic friction are 0.650 and 0.420, respectively. Will the block move under the influence of the force, and, if so, what will be the block's acceleration? Explain your reasoning.

Homework Equations

FsMAX=UsFn FkMAX=UkFn F=ma
i don't know how to make the squiggly m so i put in a U

The Attempt at a Solution

i found out that FsMAX=29.25N and FkMAX=18.9N and a=.8
but it feels like i just plugged things in and i don't really understand how these relate to each other.

 

[Vykan12]

The force of static friction is proportional to the normal force of a body. We define the constant of proportionality to be u_s.

Now when you push on a block, it will not move unless you apply enough force. This is because the force of static friction balances whatever force you apply. This is true until you reach a slipping point, which we call f_{s} max.

Mathematically, we'd say f_{s} <= u_{s}n, and we have equality when f_{s} is maximized.

Once you pass the slipping point, you have kinetic friction, and again, this force is proportional to the normal force of the object, and the proportionality constant is defined as u_{k}.

Oh, and keep in mind that the coefficient of either friction u depends on the surface in question. Ice will have a much smaller u than asphalt since it requires less force to reach the slipping point, and takes longer to get a moving object to rest (assuming the applied force is removed right after the object begins to move).

That is just a rough description, there are plenty of resources on the internet that could give you help on this topic.

 

[debbers111]

thanks! that actually helped!