Question

two forces each of magnitude 12N and 16N are inclined to each other at 45°. Find the magnitude and direction of their resultant with respect to second vector​

Answer 1

Answer:

Two forces of magnitude 10N & 8N are acting at a point. If the angle b/w the two forces is 60°, how do I determine the magnitude of the resultant force?

Don’t let change and uncertainty hold you back.

Since typing all those formulas were getting cumbersome I just solved it on a piece of paper and uploaded it.

For reference,

I have taken vector A=10N, vector B=8N, the angle between vectors A & B as

θ (theta) = 60 degrees.

The resultant vector is C and at an angle ø (phi) with vector A.

Notice another thing. I have taken ø between vector A and C. If I need to know the angle between vector B and C, say angle α (alpha)

Answer 2

Concept:

• Vectors
• An item with both magnitude and direction is referred to be a vector.
• A vector can be visualised geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector.
• The vector's direction is from the tail to the head.
• Calculating resultant vectors from given individual vectors
• Determining the direction of the resultant vector

Given:

• The first force F1 = 12 N
• The second force F2 = 16 N
• The angle between the force vectors θ = 45°

Find:

• The magnitude of the resultant vector
• The direction of the resultant vector

Solution:

We know that the resultant of two vectors A and B at an angle θ with each other is given by

R = √(A²+ B² + 2AB cos θ)

R = √(F1²+ F2² + 2F1F2 cos θ)

R = √(12²+ 16² + 2*12*16 cos 45°)

R = √(400 + 384 cos 45°)

R = √(400 + 384 * 0.7071)

R = √(400 + 384 * 0.7071)

R = √671.53

R = 25.9 N

For the direction, we use the following formula

tan ∅ = B sin θ /A + B cos θ

tan ∅ = 12 sin 45 /16 + 12 cos 45

tan ∅ = 8.485 / 24.485

tan ∅ = 0.347

The magnitude of the resultant vector is 25.9 N and the direction is tan ∅ = 0.347.

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