What Forces Are Needed to Maintain Equilibrium on a Frictionless Surface?

[ibriggs]

Homework Statement

A 5.0 Kg block at rest on a frictionless surface is acted on by forces F1= 5.5N and F2= 3.5N, as illustrated in the figure.
A) What additional force (in unit vector notation) is required to keep the block at rest?
B) What additional force (in unit vector notation) is required to accelerate the block at a rate of 2.25 m/s^2

Force 1: 3.5N at 37 degrees above +X axis
Force 2: 5.5N at 30 degrees below +X axis

Homework Equations

F=m*a
S O H C A H T O A

The Attempt at a Solution

The first step I took was to use trig functions to find the X and Y components of F1 and F2. I came up with the following:

F1X=3.5cos37=2.80N
F1Y=3.5sin37=2.12

F2X=5.5cos30=4.76N
F2Y=5.5cos30=-2.75N

Adding the X and Y components from each vector together I came to this answer for "F3" which would represent the two vectors.

F3X=7.56N F3Y=-0.63N
Then used Pythagorean theorem to find the hypotenuse (the magnitude of the new force)
which was:
7.56^2 + -0.63^2=X^2
X=7.53N

To find the angle of the new force I used:

tan^-1(-0.63 / 7.56) = -4.76 degrees

This equation gave me essentially the opposite of the angle I was looking for (if I'm thinking correctly about this problem) making the magnitude of the force to "keep the block at rest" would be -7.52N at 4.76 degrees above the -X Axis.


This answer was turned in and received a 6/10 possible points. I need help determining where I went wrong, and how I can fix it so I can turn the problem back in for a small return...not to mention it's bothering me that I don't know what I did wrong!

Thanks in advance,

Ian

 

[ibriggs]

P.s.

I think it's possible I received points off for misusing vector notation. How can I express answers in correct unit vector notation?

 

[andrevdh]

You forgot to include the weight and normal forces acting on the block.