How Do You Achieve Force Equilibrium on a Moving Object?

[starhallie]

Homework Statement

A particular object is moving on a horizontal (x,y) plane with a velocity of 10 m/s in the (+x) direction. It is simulaneously acted upon by two horizontal forces. F1= 225 N at an angle of 30 degrees with respect to (+x) and F2= 135N at an angle of -75 degrees with respect to (+x). Find the magnitude and direction of a third applied force that will leave the system in a state of equilibrium. Is the equilibrium static or dynamic? Explain your answer.

Homework Equations

I only know how to get started on this... I need help

The Attempt at a Solution

I understand that the y components are ignored since there is a constant velocity in this system and acceleration would therefore equal 0. I drew a free-body diagram with force of gravity pointing downard, normal force pointing up, and the two other force vectors. Now what?

Thank you for your help!

 

[pafala]

In my opinion, we should not consider gravity force (at least, we don't receive its mass to compute mg). Just calculate 2 force in the horizontal plane to find the 3rd force to make object is in equilibrium.

x-axis
$$\sum$$Fx = 0
F1(cos30)+F2(cos75)+F3x = 0
225(0.866)+135(0.259)+F3x = 0
F3x = -229.796 N

y-axis
$$\sum$$Fy = 0
F1(sin30)+F2(sin75)=F3y = 0
225(0.5)+(135(0.966)+F3y = 0
F3y = 17.9N

magnitude
F3 = sqrt(F3x^2+F3y^2)
F3 = 230.492N

angle
F3 angle = arctan(F3y/F3x)
F3 angle = arctan(17.9/229.796) = 4.45 degrees with respect to (-x).
(or 175.55 degrees from +x axis)

System will be dynamic equilibrium with a constant velocity of 10 m/s in the (+x) direction

 

[starhallie]

Sorry for the very late reply, pafala... thank you so much for your help on this problem. I truly appreciate it!