Question

two forces x and y are acting at 120 degrees to each other, if the magnitude are 8N and 10N respectively determine their resultant​

Answer 1

The resultant force of both forces is 15.62 N.

What is resultant?

The Resultant of forces is a single force obtained when two or more forces are combined.

To calculate the resultant of the force, we use the formula below.

Formula:

• R = √[a²+b²-2abcos∅]..................... Equation 1

Where:

• R = Resultant of the forces.
• ∅ = Angle between both forces

From the question,

Given:

• a = 8 N
• b = 10 N

Substitute these values into equation 1

• R = √[8²+10²-2×8×10cos120°]
• R = √[64+100-160cos120°]
• R =√ [164-160(-0.5)]
• R = √[164+80]
• R = √(244)
• R = 15.62 N

Hence, the resultant force of both forces is 15.62 N.

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Answer 2

Using the parallelogram law of vectors to obtain the resultant, we have the value 16 N.

What is the resultant force?

The resultant force is that force that has the same effect in magnitude and direction as two forces acting together. In this case, we have two forces , 8 N and 10 N inclined at an angle of 120 degrees

Using the parallelogram law of vectors to obtain the resultant;

R = √([8²+10²)-2×8×10cos120°]

R = √164 +80

R = 16 N

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