- #1

Lucky13ESP

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**[SOLVED] Kinetic and Static Friction**

I've done so many of these but for some reason can't figure this one out. Any help iwll be greatly appreiciated. Here is the problem:

A book of mass M = 0.55 kg rests on a table where the coefficient of static friction μs = 0.48. What is the minimum horizontal force needed to move it?

So I draw my free body diagram and get this

N=m*g

P=μs*N

where N is normal force, P is horizontal force

P = 2.59 N This part is correct

Now for the part I can't solve.

A different force of F = 3 N now acts on the book at an angle of θ = 30 deg above the surface of the table. What is the acceleration of the book if the coefficient of kinetic friction μk = 0.25?

I've tried this part two different ways. First I checked for movement

Fy+mg = N

f = μs*N

Fx - f = ma

Fx-μs(Fy+mg)=ma

3cos30-.48(3sin30+.55*9.81)=ma

-.712 N = ma since friction force > applied force, the book doesn't move so acceleration is 0. However, they don't like that answer.

So now I assumed the book must already be in motion when the force is applied which is why they give me a kinetic friction coefficient.

Fx-μs(Fy+mg)=ma

3cos30-.48(3sin30+.55*9.81)=ma

.874 N = ma

a = 1.59 m/s^2

They don't like this answer either. Can anyone helpshed some light on what I"m doing wrong? Thanks so much in advance.