four forces 10N,5N,4N and 6N
are on north , east, west and south direction. find their magnitude and direction.
forces in opposite directions will cancel , leaving net N-S and E-W forces
add the two vectors to find the resultant ... (N-S)^2 + (E-W)^2 = r^2
draw the vector diagram and use trig to find the direction angle
F = 10i + 5 + (-4) + (-6i) = 1 + 4i = 4.12N.[76o].
To find the magnitude and direction of the four forces, we can use vector addition.
1. Start by drawing a coordinate system with a point of reference, such as an origin, and label the directions: north (N), east (E), west (W), and south (S).
2. Represent each force as a vector with its magnitude and direction. Label the magnitudes of the forces as follows: 10N (north), 5N (east), 4N (west), and 6N (south).
3. To add the vectors, start from the origin and draw the first vector (10N) in the north direction.
4. From the end point of the vector, draw the second vector (5N) in the east direction.
5. To add the third vector (4N), start at the junction of the first two vectors and draw it in the west direction.
6. Lastly, draw the fourth vector (6N) starting from the junction point towards the south direction.
7. The resultant vector is the vector drawn from the origin to the end point of the last vector (6N), representing the net force.
8. To find the magnitude of the resultant vector, you can use the Pythagorean theorem. Calculate the sum of the squares of the magnitudes of the vectors (10^2 + 5^2 + 4^2 + 6^2) and take the square root of the result to get the magnitude of the resultant vector.
9. To determine the direction of the resultant vector, you can use trigonometry. Find the angle theta (θ) between the resultant vector and the positive x-axis using the inverse tangent function (θ = arctan(vertical component / horizontal component)).
10. The magnitude of the resultant vector will be the magnitude of the net force, and the angle (θ) will give the direction of the resultant vector relative to the positive x-axis.