Question

two forces 100N and 80N act at a point makeing an angle 60° between them. determine the magnitude and direction of resultant​

Answer 1

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Explanation:

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Answer 2

Answer:-

Magnitude of resultant force=156.20

Direction of resultant force=(Tan)^-1 40√3/140.

Given:-

Two forces- 100N and 80N at a point

Angle between them- 60°

To find:-

• Resultant magnitude of two forces
• Direction of resultant force

Solution:-

When two vectors are joined tail to tail then we consider that angle as angle between two vectors

Here we are given that angle between two vectors is 60°. so that's the angle between them

Magnitude and direction of Resultant force is given by the formula of vector addition

|R|=√(A)^2+(B)^2+2ABCos∅ (Magnitude)

Tanα=BSin∅/A+BCos∅ (Direction)

Let A be 100N and Let B be 80N

|R|=√(A)^2+(B)^2+2ABCos∅

|R|=√(100)^2+(80)^2+2×100×80×Cos60

|R|=√10000+6400+×2×100×80×1/2 (Cos 60°=1/2)

|R|=√24400

|R|=156.20N (magnitude of resultant force)

Now Tanα is the angle with respect to vector a

Tanα=BSin∅/A+BCos∅

Tanα=80Sin60°/100+80Cos60°

Tanα=80×√3/2/100+80×1/2 (Sin60°=√3/2,Cos60°=1/2)

Tanα=40√3/100+40

Tanα=40√3/140

∅=(Tan)^-1 40√3/140. (direction of resultant force)