The greatest and least resultant of two forces acting at a point are 16N and 4N. If they are acting at an angle 120 degrees with one another their resultant is
A. root 38N , B.root 76N, C.root 19N, D.none
F1+F2=16 ,F1-F2=4 so F1=10,F2=6 r=root over 10^2+6^2+2×10×6×1÷2 r=root 100+36+60=root 100+96 r =root 196 =14
Root 76N
✓76
The two forces clearly have magnitudes 6 and 10.
So, use the law of cosines to get
r^2 = 100+36-120(-1/2) = 196
r = 14
To find the resultant of two forces acting at an angle, we can use the formula for the magnitude of the resultant force:
Resultant = √(F1^2 + F2^2 + 2F1F2cosθ)
Where F1 and F2 are the magnitudes of the two forces, and θ is the angle between them.
In this case, the given magnitudes of the forces are 16N and 4N, and the angle between them is 120 degrees.
Plugging these values into the formula, we have:
Resultant = √(16^2 + 4^2 + 2*16*4*cos(120))
Calculating the expression inside the square root:
Resultant = √(256 + 16 + 128*cos(120))
Now, let's find the value of cosine of 120 degrees:
cos(120) = -0.5
Substituting this value back into the equation:
Resultant = √(256 + 16 + 128*(-0.5))
Resultant = √(256 + 16 - 64)
Resultant = √(208)
Resultant ≈ 14.42N
So, the magnitude of the resultant force is approximately 14.42N.
None of the given answer choices match this value, so the correct option would be D. (none).