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Forces of magnitude 2P, 4P, 3P and P act on a particle in directions parallel to the sides AB, BC, CD and DE of a regular hexagon. Find the magnitude and direction of the resultant.?
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Forces of magnitude 2P, 4P, 3P and P act on a particle in directions p...
Problem: Forces of magnitude 2P, 4P, 3P and P act on a particle in directions parallel to the sides AB, BC, CD and DE of a regular hexagon. Find the magnitude and direction of the resultant.

Solution:

To solve this problem, we need to use vector addition. We can represent each force as a vector and add them using the parallelogram law of vector addition.

Step 1: Draw a diagram of the hexagon and the forces acting on it.

Step 2: Represent each force as a vector with its tail at the starting point of the force and its head at the ending point of the force. Label each vector with its magnitude and direction.

Step 3: Using the parallelogram law of vector addition, draw the diagonal of the parallelogram formed by the vectors 2P and 4P. This diagonal represents the resultant of these two vectors.

Step 4: Draw the diagonal of the parallelogram formed by the vectors 3P and P. This diagonal represents the resultant of these two vectors.

Step 5: Add the two resultant vectors using vector addition. The magnitude and direction of the resulting vector is the magnitude and direction of the resultant force.

Step 6: Use trigonometry to determine the magnitude and direction of the resultant force.

The magnitude of the resultant force is given by:

|F| = sqrt[(2P)^2 + (4P)^2 + 2(2P)(4P)cos(120) + (3P)^2 + P^2 + 2(3P)(P)cos(120)]

Simplifying this expression gives:

|F| = sqrt(38P^2)

|F| = 2sqrt(19)P

The direction of the resultant force is given by:

theta = arctan[(3P + Psin(120))/(2P + 4Pcos(120))]

Simplifying this expression gives:

theta = arctan[(2sqrt(3) + sqrt(3)/2)/(3/2)]

theta = arctan(4sqrt(3)/3)

theta = 71.57 degrees (rounded to two decimal places)

Therefore, the magnitude of the resultant force is 2sqrt(19)P and its direction is 71.57 degrees.
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Forces of magnitude 2P, 4P, 3P and P act on a particle in directions p...
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Forces of magnitude 2P, 4P, 3P and P act on a particle in directions parallel to the sides AB, BC, CD and DE of a regular hexagon. Find the magnitude and direction of the resultant.?
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Forces of magnitude 2P, 4P, 3P and P act on a particle in directions parallel to the sides AB, BC, CD and DE of a regular hexagon. Find the magnitude and direction of the resultant.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Forces of magnitude 2P, 4P, 3P and P act on a particle in directions parallel to the sides AB, BC, CD and DE of a regular hexagon. Find the magnitude and direction of the resultant.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Forces of magnitude 2P, 4P, 3P and P act on a particle in directions parallel to the sides AB, BC, CD and DE of a regular hexagon. Find the magnitude and direction of the resultant.?.
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