A particle is at rest and experiencing 4 forces as shown fin

A particle is at rest, and experiencing 4 forces as shown, find F and theta.

Ans 2

The diagram shows 4 forces acting on a mass of 3 Kg. The 4 forces are:

(1) 40 N making an angle 35 deg with -x axis in -x , +y quad.

(2) 50N making an angle 40 deg with - x axis in -x, -y quad.

(3) force F making an angle \\theta with +x axis in +x ,-y quad

and

(4) 25N making an angle 30 deg with +x axis in +x,+y quad.

The four forces are keeping the mass at rest. Hence their resultant is zero.

Now resolving the forces in x direction we get:

-40 cos 35 + 25 cos 30 -5- cos 40 + F cos \\theta = 0

This gives

F cos \\theta = 41.4173 N ---(i)

Similarly, resolving the forces in y direction we get:

40 sin 35 + 25 sin 35 - 50 sin 40 - F sin \\theta=0

this gives:

F sin \\theta=7.1435798 ---(ii)

From (i) and (ii)

tan \\theta = 0.172478 i.e \\theta = 9.786 deg ---(iii)

Substituing (iii) in (i) we get:

F =41.4173N --(iv)

The eqns (iii) & (iv) give the desired values of F & \\theta.