Using a graphical method of getting resultant vectors, find the resultant of the following vectors: 8N along the positive X-axis and 6N making an angle of 45 degrees with the positive X-axis and 10N -20 degrees below West.
Fr = 8N[0o] + 6N{45o] + 10N[200o].
Fr = 8 + (6*Cos45+i6*sin45) + (10*cos200+i10*sin200),
Fr = 8 + (4.24+4.24i) + (-9.40-3.42i),
Fr = 2.84 + 0.82i = 2.96N[16.1o]. = Resultant force.
16.1o Above +x-axis.
To find the resultant of these vectors using a graphical method, we will need to draw a scaled vector diagram and then measure the magnitude and direction of the resultant vector.
Step 1: Draw the X and Y axes. Label the positive X-axis, positive Y-axis, and the origin (point where X and Y axes intersect).
Step 2: Draw the first vector, which is 8N along the positive X-axis. Since it is along the X-axis, it will only have an X-component. Draw the vector starting from the origin and extend it to 8 units along the positive X-axis.
Step 3: Draw the second vector, 6N at an angle of 45 degrees with the positive X-axis. To do this, we first draw a line representing the vector inclined at 45 degrees. Then, we measure the length of the vector on the line and scale it down to represent 6 units.
Step 4: Draw the third vector, 10N at an angle of -20 degrees below the West direction. Start by drawing a line representing the West direction. Then, draw a line inclined at -20 degrees below the West direction. Measure the length of the vector on this line and scale it down to represent 10 units.
Step 5: Determine the X and Y components of each vector. For the first vector (8N along the positive X-axis), the X component is 8N and the Y component is 0N. For the second vector (6N at 45 degrees), the X component is 6N * cos(45) and the Y component is 6N * sin(45). For the third vector (10N at -20 degrees), the X component is 10N * cos(-20) and the Y component is 10N * sin(-20).
Step 6: Add the X and Y components of all three vectors. The X component of the resultant vector is the sum of the X components of the individual vectors, and the Y component is the sum of the Y components.
Step 7: Calculate the magnitude of the resultant vector using the Pythagorean theorem: magnitude = sqrt(X^2 + Y^2).
Step 8: Calculate the direction of the resultant vector by finding the angle it makes with the positive X-axis. Use the inverse tangent function (tan^-1) to find the angle: angle = tan^-1(Y/X).
Step 9: Draw the resultant vector on the vector diagram using the calculated magnitude and direction.
Step 10: Measure the magnitude and direction of the resultant vector from the diagram to find the answer.
I hope this step-by-step explanation helps!
To find the resultant of vectors using a graphical method, we need to draw a graphical representation of each vector and then combine them to find the resultant.
Step 1: Draw the vectors
Let's start by drawing the first vector, which is 8N along the positive X-axis. Since it is along the positive X-axis, we draw the vector as a straight line going towards the right.
Next, draw the second vector, which is 6N making an angle of 45 degrees with the positive X-axis. To do this, draw a line that starts from the tip of the first vector and makes an angle of 45 degrees with the X-axis.
Finally, draw the third vector, which is 10N -20 degrees below West. To do this, draw a line starting from the tip of the second vector and extend it towards the West (left) direction. Then, draw a line downwards at an angle of 20 degrees from the horizontal line.
Step 2: Combine the vectors
To combine the vectors, take the starting point of the first vector as the starting point for the resultant vector. Then, draw a line from the starting point to the tip of the third vector.
Step 3: Measure the magnitude and direction of the resultant vector
To measure the magnitude (length) of the resultant vector, use a ruler to measure the length of the line from the starting point to the tip of the third vector. This will give you the magnitude of the resultant vector.
To determine the direction of the resultant vector, use a protractor to measure the angle between the positive X-axis and the line from the starting point to the tip of the third vector. This will give you the direction of the resultant vector.
By following these steps, you can find the resultant of the given vectors using a graphical method.