Question

Two forces of 6 lbs and 8 lbs act on an object. If these two forces form an angle of 60, then find the magnitude of the resultant force.

Answer 1

To find the resultant force when two forces of 6 lbs and 8 lbs act at a 60° angle, we use the law of cosines. The magnitude of the resultant force is √(36 + 64 + 96), which simplifies to 14 lbs.

Step-by-step explanation:

To find the magnitude of the resultant force when two forces of 6 lbs and 8 lbs act on an object at a 60° angle, we can use the law of cosines. The formula to calculate the magnitude of the resultant force R is:

R = √(F1² + F2² + 2 · F1 · F2 · cos(θ))

Where:

• F1 = 6 lbs
• F2 = 8 lbs
• θ = 60°

Substituting the given values into the formula:

R = √(6² + 8² + 2 · 6 · 8 · cos(60°))

This simplifies to:

R = √(36 + 64 + 96)

R = √(196)

The magnitude of the resultant force is √(196), which equals 14 lbs.

Answer 2

The magnitude of Resultant force is F = 7.21-lbs

Step-by-step explanation:

Two forces acting on an object which are named as F1 and F2.

The angle formed by the forces are 60-degrees

F1 = 6-lbs , F2 = 8-lbs

theeta = 60°

F = √F1²+F2²-2(F1)(F2)cos(theeta)

F = √(6)²+(8)²-2(6)(8)cos(60)

F = √36+64-(96)cos(60)

F = 7.21-lbs

where,

F1 = magnitude of force 1

F2 = magnitude of force 2

theeta = angle formed by forces