# Homework Help: 2D kinematics and vectors

1. Apr 26, 2014

### hri12

1. The problem statement, all variables and given/known data

A book of mass M = .55 kg rests on a table where the coefficient of static friction us = .45. A force, F = 4 N acts on the book at an angle of 15 degrees above the surface of the table. What is the acceleration of the book if the coefficient of kinetic friction uk = .23?

2. Relevant equations

ΣFx = ma
ΣFy = ma

Ff = Fn(uk)

3. The attempt at a solution

I drew free body diagrams.

ΣFx = Fx - Ff
Fx - Ff = ma(x)
Fx - Fn(uk) = ma(x)

ΣFy = ma
Fn - Fy - mg = ma(y)

I'm not sure where to go from here. I know that I need to use Pythagoras theorem when I have the values of a(x) and a(y) but I don't know how to get that far.

2. Apr 26, 2014

### SammyS

Staff Emeritus
What do you suppose the value of ay is ?

3. Apr 26, 2014

### hri12

I know it's not zero because:
2. It's being pulled diagonally upwards, so both a(x) and a(y) should have a nonzero value.

4. Apr 26, 2014

### hri12

Edit: the answer should be 5.20 m/s^2

5. Apr 26, 2014

### hri12

Never mind. Got it. Thanks everyone!!!!!

SOLUTION
ΣFx = Fx - Ff
Fx - Ff = ma(x)
Fx - Fn(uk) = ma(x)

ΣFy = ma
Fn + Fy - mg = ma(y)

a(y) = 0 (not sure why...)
Fn + Fy - mg = 0
Fn = mg - Fy

Fx - (mg - Fy)(uk) = ma(x)
a(x) = (Fx - (mg - Fy)(uk) )/m
a(x) = 5.2

((5.2)^2 + (0)^2)^(1/2) = 5.2

6. Apr 26, 2014

### SammyS

Staff Emeritus
Excellent !
Then this is worth looking at further.

ay can possibly be positive, but it can't be negative. Right ?

If ay > 0, then the normal force will be zero. Right? Then Fy - mg = ay > 0 . Is Fy - mg > 0 ?

If that's not the case, then your solution with ay = 0 is correct.

7. Apr 27, 2014

### hri12

Why will the normal force be zero? If anything the normal force will be Fn = ma(y) + mg -Fy...

I still don't understand.

8. Apr 27, 2014

### SammyS

Staff Emeritus
I may not have stated that too clearly.

Why is there any normal force? It's there because the surface of the table keeps the book from accelerating downward through the surface. So the surface exerts whatever force is needed for this to be the case.

The normal force cannot be negative. If it were, it would be pulling down on the book.

If ay is positive, then the book is no longer on the surface of the table thus no normal force

9. Apr 28, 2014

### hri12

So basically because the book isn't moving in the y direction? That makes sense.

Thank you so much btw for all of your help. :)