calculate the magnitude and direction of the resultant of two vectors 5N and 7N inclined at an angle 30° to each other
Lets measure angles from the 7N vector.
R=7@0 + 5@30=7@0 + 5*cos30@O + 5Sin30@90
so figure each of those out, and combine the two at zero degrees.
magnitude:
sqrt((@zerosum)^2+(@90vector)^2)
direction:
arctheta [(@90vector)/(@0vector)]
Fr = 5[0o] + 7[30o].
X = 5 + 7*Cos30 = 11.1 N.
Y = 7*sin30 = 3.5 N.
Fr = X + Yi = 11.1 + 3.5i = 11.6N.[17.5o]. = Resultant force.
To calculate the magnitude and direction of the resultant of two vectors, you can use the laws of trigonometry. Here's how you can solve this problem step by step:
Step 1: Draw a diagram
Draw two vectors representing the given magnitudes and angles. Label one vector as 5N and the other as 7N, making sure to show the angle of inclination (30°) between them.
Step 2: Resolve each vector
Resolve each vector into its horizontal and vertical components using the trigonometric formulas:
- For the horizontal component, use the formula: V * cosθ, where V is the magnitude and θ is the angle.
- For the vertical component, use the formula: V * sinθ.
For the 5N vector:
Horizontal component = 5N * cos30°
Vertical component = 5N * sin30°
For the 7N vector:
Horizontal component = 7N * cos30°
Vertical component = 7N * sin30°
Step 3: Add the horizontal and vertical components
Add the horizontal components of both vectors together, and add the vertical components of both vectors together.
Horizontal component of the resultant = (Horizontal component of 5N vector) + (Horizontal component of 7N vector)
Vertical component of the resultant = (Vertical component of 5N vector) + (Vertical component of 7N vector)
Step 4: Find the magnitude
Use the Pythagorean theorem to find the magnitude of the resultant vector:
Magnitude of the resultant vector = sqrt((Horizontal component of the resultant)^2 + (Vertical component of the resultant)^2)
Step 5: Find the direction
Use the tangent of the angle between the resultant vector and the horizontal axis to find the direction:
Direction of the resultant vector = arctan((Vertical component of the resultant)/(Horizontal component of the resultant))
By following these steps, you will be able to calculate the magnitude and direction of the resultant vector for the given problem.