Motion of a Block with Three Forces

[fubag]

The diagram below shows a block of mass m=2.0\; \rm kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F_1 = 4.0\;{\rm N}, F_2 = 6.0\;{\rm N}, and F_3 = 8.0\;{\rm N} are applied to the block, initially at rest on the surface, at angles shown on the diagram.

1. Calculate the magnitude of the total resultant force \vec{F}_{\rm r} = \vec{F}_1+ \vec{F}_2 +\vec{F}_3 acting on the mass.

2. What angle does F_r_vec make with the positive x axis?

3. What is the magnitude of the mass's acceleration vector, a_vec?

4. What is the direction of a_vec? In other words, what angle does this vector make with respect to the positive x axis?

5. How far (in meters) will the mass move in 5.0 s?

6. What is the magnitude of the velocity vector of the block at t = 5.0\;{\rm s}?

7. In what direction is the mass moving at time t = 5.0\;{\rm s}? That is, what angle does the velocity vector make with respect to the positive x axis?I just need clarification on how to start this problem...do I simply use Fnet = ma? and to find the resultant I am assuming I need the magnitude of vectors formula, but how do I use it here?

any help will be greatly appreciated.
http://img216.imageshack.us/img216/6486/1206lb2.th.jpg

 

[Doc Al]

I just need clarification on how to start this problem...do I simply use Fnet = ma?

Sure.

and to find the resultant I am assuming I need the magnitude of vectors formula, but how do I use it here?

Just find the components of each force and add them up.

 

[dlgoff]

Hint to start with. Break down the forces into their x and y components. Then find the resultant force from these. Rember you'll need to make use of the sin and cos of your angles.

 

[fubag]

ok

so this is what I got:

f(->)1: 3.63i + 1.69j
f(->)2: 4.91i - 3.44j
f(->)3: 8i

Now to determine the resultant, I just add all of these up?

I get then f(->)r: 16.54i - 1.75j

so resultant magnitude is = 16.63 N??

 

[Doc Al]

Add up the components and you have the components of the resultant. (Double check the signs of your components.)

 

[fubag]

ok sorry

the 3rd one has -8iSo then it should be 1.83 N?