Find the resultant of two vectors 7N and 8N inclined at an angle of 65 degree to each other
One can derive from the law of cosines:
c = sqrt[a^2 + b^2 + 2ab cos65]
= sqrt[49 + 64 + 56*0.4226] = 12.66
c is the long diagonal of the force parallelogram, i.e the resultant
One can also do it with components. The resultant of
(7 + 8 cos65)i and 8 sin65 j is
sqrt(10.381^2 + 7.251^2] = 12.66
To find the resultant of two vectors, we can use the parallelogram law of vector addition. This law states that if two vectors are represented by adjacent sides of a parallelogram, then the diagonal passing through their common point represents the resultant vector.
In this case, we have two vectors: 7N and 8N, inclined at an angle of 65 degrees to each other. To find their resultant, follow these steps:
Step 1: Draw the vectors
Draw a line segment to represent the first vector of magnitude 7N. Starting from its initial point, draw the second vector with a magnitude of 8N, making an angle of 65 degrees with the first vector.
Step 2: Complete the parallelogram
Complete the parallelogram by drawing lines parallel to the vectors from their respective endpoints. This will create a parallelogram with the vectors as adjacent sides.
Step 3: Draw the resultant vector
Draw the diagonal passing through the common point of the vectors. This diagonal represents the resultant vector.
Step 4: Measure the magnitude and direction
Measure the length of the resultant vector using a ruler. The magnitude can be determined by the scale you are using for the diagram.
To find the direction of the resultant vector, measure the angle it makes with the first vector. This angle can be measured using a protractor or by measuring the angle made with a reference line (e.g., horizontal line).
In this way, you can determine the magnitude and direction of the resultant vector, given the two vectors and their inclination angle.